Senior Richard Klein scored the game-winning goal in OT with the assist coming from Matt Hamm in his first game for Baker.
The game was scoreless until the 86th minute when Ashford's Lucas Almeida scored a goal past Baker keeper Matt Bickley.
Then less than two minutes later, sophomore Amer Didic slipped the ball past Ashford keeper Patrick Kinsella to tie things up.
The Wildcats took 14 shots as a team with seven on goal. Cameron Zimmerman and Chris Tuso led the team with three shots.
Ashford took 11 shots with six on goal and Bickley had four saves in goal for Baker.
Baker will hit the pitch again on Sunday in its home opener against AIB College of Business at 2:30 p.m. at North Park. Live stats will be available at www.bakerwildcats.com.