Keith Wallis, 53, of West Drayton, west London, sent an email to Conservative deputy chief whip John Randall, who was his MP, wrongly claiming that he had seen what happened as Andrew Mitchell left Downing Street on September 19, 2012.
Last month, the officer from the Metropolitan Police diplomatic protection group pleaded guilty at the Old Bailey to misconduct in a public office.
The court heard he admitted his lie in a police interview and offered to resign.
Mr Mitchell, then chief whip, became involved in a heated confrontation with another police officer, Toby Rowland, after he was refused permission to cycle through the main gate of Downing Street.
Following reports of the incident in 2012, the Sutton Coldfield MP apologised for being disrespectful to police but denied Pc Rowland's claim that he used the word ''pleb''.
But his apology was not enough to prevent members of the Police Federation of England and Wales protesting at the Conservative Party's annual conference in T-shirts bearing the slogan "Pc Pleb and Proud".
After meeting the MP in Sutton Coldfield, the federation's Inspector Ken MacKaill said he had "no option but to resign", while Labour leader Ed Miliband described him as "toast" in the House of Commons and Prime Minister David Cameron himself said his chief whip was wrong to use the words he did.
The unrelenting pressure eventually led Mr Mitchell to offer his resignation on October 19, a month after the initial altercation.
Following Wallis's guilty plea last month, Mr Mitchell said justice had been done and there were calls for his return to Government.
Met commissioner Sir Bernard Hogan-Howe apologised to Mr Mitchell and said that Wallis's behaviour fell "way below the standards expected" of his officers.
Mr Cameron also issued a statement saying it was "completely unacceptable" for police to falsify their account of an incident.
Mr Justice Sweeney said: "Passing sentence on you I am in no position to decide precisely what happened between the officers and Mr Mitchell in Downing Street nor do I need to do so, but it is absolutely clear what did not happen - you were not an independent member of the public, you were not present, neither was your nephew, and neither of you witnessed the incident.
"Yet, over a total period of nearly three months you pretended to your Member of Parliament and initially to the interviewing officers that all of those things were true including involving your nephew in the process."
Mr Sweeney went on: "This was thus sustained, and in significant measure, devious misconduct which fell far below the standards expected of a police officer. Indeed it was a betrayal of those standards, and was misconduct which as well as having had an impact Mr Mitchell himself, has had a significant impact on public trust and confidence in the integrity of police officers."
He added that police officers "must be deterred from misconduct and the public must be able to see that punishment will be visited upon police officers who betray the trust reposed in them".
Earlier, the court heard that "rumour and gossip" incensed Wallis, and combined with high emotions over the killing of two female officers in Manchester the day before.
It was in this state that Wallis got drunk after his shift and went home to send the late night email full of spelling mistakes and capital letters to Mr Randall.
Despite stating he did not believe Mr Mitchell should lose his job, events "got completely out of hand", his lawyer Patrick Gibbs QC said.
Mr Randall's interest in the case in Westminster, combined with media involvement, escalated the situation and Wallis did not have the mental capacity to come clean and put a stop to it, the court heard.
He was caught out in the lie when CCTV showed he was not at the Downing Street gates with his nephew at the time of the row with Mr Mitchell, as he had claimed.
But Mr Gibbs insisted there was no conspiracy at play, rather Wallis had convinced himself he had witnessed the incident on September 19 2012.
Mr Gibbs said: "While it is impossible to pinpoint the moment Mr Wallis came to believe that video in his head, he did genuinely come to believe it."
Mr Gibbs said Wallis, who served for 30 years, suffered from both mental and physical illness and had been deeply affected by the death of his father, who was also a police officer.
Appealing to the judge not to send him to jail, Mr Gibbs said: "He would be the ideal scapegoat for more sophisticated men but sending him to prison would be to mistake this for what it is not."
Wallis's emails to Mr Randall were read out by prosecutor Zoe Martin.
In the email of September 20, he says: "I write to complain at the absolutely digesting (sic) behaviour displayed by your fellow member of parliament."
He goes on to describe going to Downing Street with his nephew who was visiting from Hong Kong in the hope of seeing the Prime Minister.
The nephew spotted Mr Mitchell and mistook him for London mayor Boris Johnson engaged in what Wallis described as "yobbish and loutish" behaviour.
Describing himself as a driver, Wallis wrote that tourists were "shocked" at the row and some were filming it.
He said Mr Mitchell was swearing and made the now disputed claim that he called an officer a "pleb" as he was barred from cycling through the main Downing Street gate.
Complaining at Mr Mitchell's "unacceptable behaviour", he says: "If you are in a position of authority you can say whatever you like to the police because you are more important than anybody else."
Wallis wrote that he "did not expect anything to come of it" but Mr Randall did take up the complaint and tried repeatedly to get hold of his constituent.
An investigation got under way at Westminster and a story ran in The Sun the following day.
As the situation intensified, a Channel 4 news team went to his home and confronted him about the email. Wallis claimed not to know about it.
By December, Wallis seemed upset at work and his sergeant suggested he take time off, the court heard.
Wallis told a member of the Police Federation about contacting his MP because he was "disgusted by the incident", saying he had not mentioned he was a police officer.
Police who were investigating the incident eventually found out Wallis was a constable and he was arrested for misconduct in a public office.
Wallis told officers: "I knew I should have thrown myself under a train yesterday."
Initially Wallis stuck to his story but when confronted by the CCTV evidence, he came clean, the court heard.
He told police: "I eventually convinced myself I was there...I totally believed I was there.
"I thought in a stupid, naive pathetic way I was backing up my colleagues. I just convinced myself I was there."
He went on to apologise for letting down the Metropolitan Police, his family and Mr Mitchell.
Zoe Martin said that Wallis was "mortified by the disgrace" of his actions.
After the sentencing, Sir Bernard said that Wallis, who is one year away from retirement, would now be the subject of a misconduct process "as soon as possible".
He said: "Pc Wallis's actions have clearly fallen way below the standards that me, my fellow police officers and the public demand.
"I expect my officers to serve the public without fear or favour. Where officers break the law they must expect to be held to account and answer for what they have done.
"Yesterday I apologised personally to Mr Mitchell that an MPS officer clearly lied about seeing him behaving in a certain manner. Today, I apologise to the public for Pc Wallis's behaviour."
Two officers from the DPG have received final written warnings and a third officer has undergone management action in relation to inappropriate comments, the Metropolitan Police confirmed.
Wallis, along with four other officers from DPG, will be the subject of gross misconduct hearings due to start at the end of the month.
John Tully, chairman of the Metropolitan Police Federation said: "It is hugely regrettable that Pc Wallis decided to take the course of action he did in respect of his having witnessed the Downing Street incident (Plebgate).
"His actions have undermined public confidence in the police service in general and have muddied the waters in respect of the original incident. He has admitted his guilt in the criminal proceedings and must face the consequences.
"It must be emphasised that the great majority of police officers display courage and dedication in their daily duties and work tirelessly and honestly to keep their communities safe."