Five seconds into the power play, B.U. senior winger Chris Heron redirected a shot from the point past Prestifilippo to pocket his 12th goal of the season.
Baker added an empty-net goal with 15 seconds remaining in the third to snare the hat trick after Harvard failed to register a shot on net with a 6-on-4 advantage to end the game.
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The Crimson will face Northeastern next Monday night in the Consolation round of the Beanpot.
Northeastern lost a lopsided game to Boston College earlier in the day, falling to the Eagles, 6-0.
B.U. will meet the B.C. for the 14th time in the finals of the Beanpot next Monday night as well.