Senior designated hitter Dustin Kremer's sacrifice fly pushed home the decisive run in the Owls' 8-7 win over the Wildcats on Saturday.
The Owls (10-3) have won five in a row.
William Woods led 6-2 midway through the seventh inning, but Baker responded with six runs in the bottom of the frame to grab a one-run edge.
Owls senior center fielder Cody Stewart tied the game at 7-all on a one-out sacrifice fly to left field that scored senior shortstop Stephen Kohler.
Junior John Cavness - one of 11 William Woods pitchers used - threw 1 2/3 innings to earn the relief win. Cavness struck out four, while allowing one run.
Sophomore second baseman Alex St. Pierre and junior catcher Grant Garrett each went 2-for-3 with a run scored. Junior left fielder Larry Price was 2-for-4 with a run scored, while Kremer was 1-for-3 with two RBIs and a run scored.
The Owls outhit the Wildcats 11-10.
William Woods' three-game set at Freed-Hardeman to open American Midwest Conference play was cancelled. The Owls host Culver-Stockton in their home opener at 2 p.m. today.