Lee Goren, Jesse Schultz and Jason Jaffray also scored for the Moose, while Chris Lee and Kris Chucko scored for Omaha. Defenceman Chris Lee gave Omaha the early lead with a shot from the point for his first AHL goal 81 seconds into the game, and Chucko made it 2-0 when he intercepted a pass, sped down the right wing and fired a shot past goalie Wade Flaherty for his 10th goal late in the period.
Manitoba began its comeback in the second period when Goren beat Curtis McElhinney with a hard wrist shot. Up to that point, McElhinney had seen just five shots on goal.
The Moose tied it in the last second of the period when Schultz banged in his own rebound.
Bolduc cruised into the slot and beat McElhinney with a soft backhander 2:22 into the third period, and Jaffray added a power-play goal into an empty net in the last minute.
The teams meet again in the MTS Centre on Wednesday.