The British number one delighted a packed Centre Court as he delivered a 6-1 6-4 7-5 victory in two hours and two minutes.
Murray, who will now face Slovenian Blaz Rola on Wednesday, was touched by his reception at the All England Club.
"It brought back a lot of good memories. It is nice to walk out to a full crowd for the first match," he said.
"Last year was the best memory I have had, but I have had a lot of tough moments on that court as well so there is a lot of things I think about."
Rola, meanwhile, admits he does not know what to expect when he takes to Centre Court for the first time, if the match is to be played there.
"Nothing can prepare me for this," he said after beating Pablo Andujar of Spain in straight sets on Court Five.
"I am going to walk up that stand and see how many people are actually watching this because I actually really never stepped on the Centre Court here."
Elsewhere on day one, 18th seed Fernando Verdasco of Spain lost to Australian Marinko Matosevic, with the 2013 Wimbledon quarter-finalist going out in four sets, 6-4 4-6 6-4 6-2.
"Tennis is like this. I tried to play my best and I didn't win. That's it," Verdasco said.
On Court Two, sixth seed Tomas Berdych came back from losing the first set to beat Victor Hanescu of Romania 6-7 (7/5) 6-1 6-4 6-3.
Ernests Gulbis, the 12th seed from Latvia, beat Estonia Jurgen Zopp 7-6 (9/7) 7-5 7-6 (12/10), while Australian Bernard Tomic came through in straight sets against Russian Evgeny Donskoy, 6-4 6-3 6-2.
However, number 25 seed Andreas Seppi of Italy lost 6-3 2-6 6-4 7-6 (7/5) 6-4 to Argentina's Leonardo Mayer.
British wild-card James Ward went down in straight sets to Mikhail Youzhny, the 17th seed from Russia.
Ward, set to pocket £27,000 in consolation after being handed a place in the first round, said: "I thought he played very well and executed his game. I obviously didn't play as well as I would hoped. That was about it, but you've got to take the loss on the chin and move forward."