An amazing Stuart Hogg drop-goal from 40 metres rescued the Warriors from a sticky situation in the Showgrounds on Saturday, completing a man of the match performance with ball in hand and with the boot.
Despite tries from Tommy Seymour, George Turner and Ryan Wilson, Warriors trailed 26-17 with 20 minutes left and had Adam Hastings in the sin-bin.
A late Adam Ashe try and those three points from Hogg's boot rescued Glasgow on a day when ill-discipline and raggedness threatened to undermine them.
Even allowing for Glasgow's spirited comeback, Connacht could still have won it in the last second when Craig Ronaldson hit a post from a long-range penalty.
