However, the absence of a four-try bonus point means that even an Amlin Challenge Cup spot is highly unlikely.
The Scottish outfit had tries from Tom Brown, Cornell Du Preez and Dougie Fife plus a 12-point contribution from skipper Greig Laidlaw, while Maxime Delonca touched down for Perpignan and Wales international James Hook - deployed at full-back on this occasion - landed three penalties and a conversion.
Edinburgh had the better of the opening exchanges without threatening the Perpignan line and reverted to the trusty boot of Laidlaw to open the scoring, the scrum-half slotting a straightforward penalty after the visitors failed to roll away after the tackle.
The hosts extended their lead five minutes later when Tom Brown pounced as the ball squirted out at the breakdown and sprinted in, leaving Laidlaw a simple conversion to hoist the tally into double figures.
Perpignan had not yet visited the home 22, but they opened their account when Hook booted a penalty from 35 metres. And they appeared to have rumbled over for a try after a close range lineout but the referee ruled out the score after consulting the television official.
A spell of sustained pressure eventually by the French outfit ended when Willem Nel hit Dan Leo with a thumping tackle and drove the Perpignan flanker backwards, but the momentum remained with the visitors and a late tackle by Jack Cuthbert handed Hook a simple three points.
From the restart, Edinburgh won a penalty but Laidlaw was off target with a poorly struck effort.
However, he atoned for that miss shortly before the break, stroking over his next attempt to see the home side into a 13-6 lead at half-time.
The visitors resumed strongly and the hosts were fortunate to escape without conceding after a Laidlaw clearance was charged down. However, the score eventually came courtesy of Hook, who hammered over a long-range penalty.
Perpignan failed to build on that score and Edinburgh were soon back on the offensive. The visitors lost hooker Guilhem Guirado to the sin bin and the hosts took immediate advantage of their numerical advantage, Fife feeding Du Preez who crashed through the final tackle to touch down.
Laidlaw's sweetly struck touchline conversion took the score to 20-9 with half an hour to play.
And the third try came shortly afterwards when Carl Bezuidenhout chipped ahead, Du Preez followed up with the lightest of touches and Fife profited from a fumble by Wandile Mjekevu to pick up and dive over. Laidlaw again added the extras.
That score in the 57th minutes sparked the chase for the bonus-point try. However, the hosts allowed their opponents to regain the initiative and a series of attacks culminated in a try for Delonca, with Hook adding the conversion from wide on the left.
With five minutes to play, home coach Alan Solomons had his final throw of the dice when he emptied his bench in pursuit of the fourth try but his efforts were to no avail.