Nathan Smith scored on the power play 4:32 into the match and Alexandre Bolduc made it 2-0 seven minutes later for Manitoba (15-13-4-4).
Duncan Milroy replied with a man-advantage goal 15:45 into the second period for Hamilton (21-10-1-1), which moved a point ahead of Rochester for first place in the North Division. Jonathan Ferland tied the match for the Bulldogs with 1:24 remaining before the second intermission.
That was all of the scoring until the shootout, where Grabovski put it by Moose goalie Wade Flaherty on Hamilton's fourth shot.
Bulldogs goalie Haroslav Halak blocked 28 shots in regulation and overtime, and then all five in the shootout.
Flaherty made 27 saves over the game's first 65 minutes.