It proved, beyond question, that the Tynecastle club possess enough, even at this early stage of their rebuilding process, to trouble Rangers on the field and will have reinforced the status of Robbie Neilson, their head coach, within his own dressing-room as much as anywhere else.
It may have been no more than 90 minutes of what will be a long and intriguing campaign, but, from the perspective of Steven Pressley, who played for both clubs and has detailed knowledge of Scottish football's second-tier from his time as manager of Falkirk, it was significant.
Pressley believes Neilson, a man he tried to recruit for Coventry City as under-18s coach last year, has everything required to win the SPFL Championship title.
Victory on the south side of Glasgow was important in terms of building the momentum necessary to power a title-winning campaign and convincing the players to commit themselves to his vision of the future.
The stability and organisation that Neilson, still finding his way in his first major job as a coach, requires appears to be in place.
Hearts have emerged from the financial meltdown that brought the Vladimir Romanov era to a cataclysmic halt with their chairwoman, Ann Budge, and the Foundation of Hearts group operating a solid, sustainable business model. Craig Levein has developed a footballing philosophy, if you like, for all levels of the club in his role as director of football. Everyone, on the face of it, knows where he or she stands.
Compare that with the situation Ally McCoist is dealing with in his role as manager of Rangers. The ever-unfolding chaos within the club's powerbase has been well-documented and only looks like growing worse, with the need to raise fresh funds painfully clear and Charles Green, now a sworn enemy of the manager, back on the scene with a claim that he has £10m of investment behind him.
The former director Dave King is still investigating potential routes to stage a takeover in the background while the money being siphoned out of the club by certain individuals remains nothing short of a scandal.
Of course, the team on the park does not give the impression of being value for money either. Plenty has been spent on the Rangers first team in recent years, but the capture of nothing more than the Third Division and League 1 titles could surely have been achieved with a far more moderate outlay.
There may not be an awful lot between Rangers and Hearts on the pitch, but they are rather different animals off it. Pressley believes that may count for something should the upcoming campaign, as he suspects, prove to be a close-run thing.
"This is going to be a real test for Alistair and his team this season," said the Coventry manager, currently rated the bookmakers' favourite for the vacant position at Huddersfield Town.
"Hearts have a young side, in many respects, but their players have decent experience and they possess a real energy, in my opinion.
"They gave a really professional, mature and organised performance at Ibrox. I certainly wouldn't want to put pressure on Robbie, but I think Hearts have a real chance of winning the league this season under his stewardship.
"From the outside looking in, Hearts appear very comfortable with the organisational model that has been created there.
"At Rangers, there is a lot of uncertainty about the ownership and the boardroom, for example. No matter what anybody says, that does filter through.
"If you look at lots of successful clubs, they get it right at the top end and that lets the football department do what it does best.
"Alistair hasn't just been a football manager for the past three years. He has been a politician and that can become very tiring. I happen to think he has handled it brilliantly, but there is no question that, for him and the club, there has to be stability above him. The team will be there challenging, for sure, but I have never been convinced with the argument that they will run away with the Championship.
"There are young assets on the pitch that not only have value, but that I believe can go on to win the club silverware."
Isn't Pressley putting too great an emphasis, though, on one victory at Ibrox on the first weekend of the league season? "You can be a terrific coach but you don't get the 'buy-in' of the players as quickly if results don't come," he explained.
"If your coaching methods are good and thorough and you start winning games, the momentum comes and it is hard to stop.
"A result like that one at Ibrox gets you the immediate 'buy-in' from the players and that is a huge thing as a manager. I think it was a very significant result for the team, but also for Robbie, who has worked tirelessly with that group."
The combination of a head coach and a director of football has never really operated smoothly within the confines of Scottish football, but Pressley believes the way in which Hearts put their current structure together should prevent the usual clashes and confusion.
"These systems will work as long as the director of football is there before the manager," he said. "A lot of the scenarios that haven't worked have seen a manager in position and then having someone parachuted in to stand behind his shoulder.
"Craig employed Robbie. That meant he came in under no illusions over how the process works. For me, it is a very good model. It is just about how you implement it initially. Robbie has a terrific relationship with Craig and is very comfortable about it all."
While Neilson is fresh to the job and able to implement his ideas free of any great political pressure, McCoist is already in the trenches. Pressley accepts that questions over his former team-mate's position will intensify should results and performances fail to improve, but believes greater recognition should be given to what he has achieved in the circumstances at Rangers.
"Alistair knows the type of job he is in," said Pressley. "Like any manager, he will come under pressure if he doesn't get results, but I don't think people have given him any real credit for his record. I know we are talking about the lower leagues, but going through last season unbeaten was phenomenal whatever the level of opposition."
Pressley does not want to create the impression he is only concentrating on the title aspirations of his former clubs, though. He believes Hibernian, endeavouring to change their image under a new chief executive in Leeann Dempster and the subject of at least one solid takeover offer, have shown commendable forward-thinking in bringing in Alan Stubbs from Everton as manager.
"Alan is probably going to have to introduce players and that takes time, but I think Hibs have made a really good choice in a really progressive manager," he said.
"He should not be judged immediately, though, because I think that has been Hibs' problem for too long. He needs time to implement his methods and philosophy and they must trust him because that is a club that needs rebuilt."