This victory, built on a sometimes magnificent defensive performance, was not enough to keep the capital side in the Heineken Cup, but it did leave them with an outside chance of reaching the last eight of the second-tier Amlin competition.
The maths are daunting. So, too, the opposition. To get through to the knockout stages, Edinburgh will have to beat Munster in Limerick, one of the most spine-tingling arenas in European rugby. In their favour, perhaps, is the fact that Munster have already won Pool 6, but the fact the Irish side will be determined to secure a home quarter-final should not be discounted.
"It was a great defensive effort and overall a really good performance," said Edinburgh head coach Alan Solomons. "I thought we deserved the result.
"I don't think we're frustrated that we didn't get a bonus point. We are a little disappointed because we had three chances to get a fourth try and couldn't take them. But I don't think we should allow that to detract from an outstanding performance."
When Dougie Fife raced through for Edinburgh's third try after 57 minutes, collecting that bonus point looked like something Edinburgh would do at their leisure over the final quarter. However, the steam seemed to go out of their performance, and they also had to cope with a resurgent Perpignan side who seemed to be fortified by their raft of late replacements - and, perhaps, the shame of what had been a feeble performance up to that point.
Certainly, the Catalans had come off second best by some distance in the forward battle. They hit the rucks hard enough, but they were regularly blasted off the ball by the power of the Edinburgh front five and the craft of the Edinburgh back row. Dave Denton, Roddy Grant and Cornell du Preez all put in magnificent shifts, and the three now form a breakaway unit that would be the envy of many sides throughout Europe.
It was only for 10 minutes during the second quarter, and for another brief period near the end, that Edinburgh did not have the upper hand. They started powerfully, shrugged off Perpignan's fitful revival, and took their scores cleverly.
Still, there was a huge dollop of good fortune about the way Edinburgh created their first try. It arrived in the 16th minute and it came after winger Fife had appeared to butcher a chance by getting himself isolated. However, when the Perpignan players poured into the breakdown to try to win the ball after Fife had been stopped, all they succeeded in doing was popping the thing into the arms of Tom Brown. As they did so, they left a huge gap around the fringe of the ruck, and Brown simply rocketed through to score.
Fortuitous and flattering as it was, Edinburgh had still dominated the game up to that point. It is only recently that they needed a 20-point deficit before they started to play, but there was a boldness and confidence about them right from the off. It helped, too, that dry conditions made for a more stable surface than has been the norm at Murrayfield lately, although that factor was probably a greater benefit for Perpignan than it was for the home side. By the time of Brown's try, Greig Laidlaw had already nudged Edinburgh ahead with his opening penalty after 11 minutes and his conversion, took them into double figures. However, it also had the effect of shaking Perpignan out of their torpor. Over the next 15 minutes, the French side began to apply some pressure and were rewarded by a couple of successful penalties by James Hook.
The Welshman was used at full-back, allowing Tommy Allan to turn out at fly-half. Allan, the former Scotland Under-20 playmaker, created controversy recently when he opted for Italy at senior level, but there was little in the Perpignan pivot's performance that would have caused wailing in the crowd over his decision. In fairness, he was playing behind a beaten pack for most of the time, and Edinburgh took advantage as they piled forward in the third quarter. Laidlaw and Hook exchanged penalties to maintain the four-point gap, but increasingly it was the Edinburgh pack who dictated the shape of the contest.
Du Preez claimed Edinburgh's second try in 47 minutes, cutting inside and blasting over the line when he had Brown running an overlap line outside him. At that point, Perpignan captain Guilhem Guirado had just been sent to the sin-bin, and Edinburgh took advantage again when they sent Fife over for the third try.
But that was it from Edinburgh. Just when it seemed they were going to kick on for the fourth touchdown, they lost a little of their edge and allowed Perpignan back into things. Replacement hooker Maxime Delonca barelled over for a try with six minutes left and, as desperately as they tried, Edinburgh could not respond at the other end. But they will be up for the fight again next weekend. After their troubled start to the season, the fact they are still alive in Europe is a considerable achievement in itself.
Edinburgh: J Cuthbert (C Bezuidenhout 40); D Fife, N De Luca, B Atiga, T Brown; G Tonks; G Laidlaw (capt; G Hart, 75)); A Dickinson (W Blaauw, 65), R Ford (A Lutui, 75), W Nel (G Cross, 26), G Gilchrist, I Van Der Westhuizen (O Atkins, 55), C Du Preez, R Grant (T Leonardi, 70), D Denton.
Perpignan: J Hook; R Haughton, L Mafi, S Piukala, W Mjekevu; T Allan (J Michel, 58), D Duvenage; S Taumalolo, G Guirado (capt), P Ion (K Pulu, 58), S Vahaamahina (G Vilaceca 40; M Delonca 62)), L Charteris (L Narraway, 62), D Leo, J-P Perez, K Chateau.
Referee: P Fitzgibbon (Ireland)