After a tight opening period in blustery conditions, Connacht took a 6-0 lead into the break but looked to be in trouble when Ander Monro halved the deficit within five minutes of the restart.
But Connacht, who had twice crossed but failed to ground the ball in the opening half, dug deep and Edinburgh never looked like getting in for a try. Monro, who replaced the injured Brendan Laney after 21 minutes, was off target with two long range penalties as Michael Bradley’s men took the game to the Scots.
Eric Elwood, starting his 16th campaign for Connacht, edged them in front after five minutes and added another from the 10 metre line five minutes from the break.
Connacht stepped up several gears in the final quarter and were finally rewarded when replacement hooker John Fogarty got the touchdown four minutes from time after another great surge by the Connacht pack.