Between injury and Ireland commitments, Mark McCall's squad was light 12 players taking on a side laden with internationals. But Ulster displayed passion, patience and played some terrific rugby as well as some early-season rustiness.
After some jittery opening play, Edinburgh got a three point reward from Chris Paterson when Ulster strayed offside. Edinburgh were well on top during the first quarter, but Paul Steinmetz landed an opportunistic drop goal against the play to level matters.
However, further Edinburgh possession led to a brace of penalties converted by Paterson to stretch Edinburgh out to a six point lead. Nonetheless, Ulster got the first try of the night. A handling error by Alistair Hogg enabled Ulster to feed Wallace and his perfectly weighted chip was reached first by Andrew Maxwell.
And it could have been better for Ulster, for whom Bell, Maxwell and Bowe were looking threatening. Bowe ran very well off a brilliant Paddy Wallace counter attack but lost the ball over the line as he tried to touch down.
Ulster delight was tempered when flanker Neil Best lost his, however. A period of 10 minutes in the bin was his reward for punching Allan Jacobsen. Ulster escaped further immediate damage when Paterson missed the penalty attempt.
Hogg atoned somewhat for his earlier error when figuring prominently in a superb try for the Scots captain Blackadder. Paterson's conversion gave Edinburgh a very useful-looking eight-point lead.
Wallace reduced this to five with half an hour to go with a successful penalty and a further effort reduced it to two, setting up the dramatic denouement.McCall was understandably delighted afterwards, saying "We shouldn't underestimate how good a performance that was against an Edinburgh team who had their internationals back. Everybody knew beforehand that we had a few problems of our own but the players who took part were magnificent. In a competitive situation, we saw plenty of passion and the players were thoroughly deserving of their victory. At times we played some great rugby and couldn't finish off some promising moves".