The Cougars sealed the deal when linebacker Jamael Green intercepted Baker quarterback Sam Vossen's pass with 2:23 left. The Cougars (9-3) were able to control the ball and run out the clock afterward.
Saint Francis will travel to Marian University in Indianapolis on Saturday for the second-round game.
The Cougars' defense forced three turnovers and turned the first two into points. Linebacker Quinn Doan intercepted a Vossen pass on Baker's first possession of the game. Saint Francis took advantage on offense with Josh Miller putting the Cougars up 7-0 on an 11-yard touchdown pass to Colin Harruff. Later, Matt Smith's fumble recovery led to one of three Emerson Ueber field goals.
Miller, who left the game with a leg injury in the third quarter, completed 10 of 16 passes for 86 yards and ran for 33 yards, including a 13-yard touchdown run. Antoin Campbell led Saint Francis with 95 yards. Saint Francis' defense was led by Brody Kalbaugh's 18 tackles.
Vossen was 17 of 29 for 204 yards as Baker finished the season 8-3.