Shenandoah (12-7, 6-5 ODAC) broke a 5-5 tie with three runs in the seventh to down W&L (11-14, 5-9).
Baker had drawn a one-out walk and advanced to third on a wild pitch.
Keegan Woolford put SU up by three runs one batter after Kroll's single with a two-run home run to right.
The blast is his second of the season.
Gerard DePhillips got his seventh save of the year by pitching a scoreless ninth. He struck out two and got the final out on a comebacker to the mound.
Kroll had four of the Hornets nine hits with Baker and Woolford both driving in a pair.
Kenneth Hartzfeld (0-3) took the loss for the Generals. He allowed one run on one walk in 1/3 inning.
Shenandoah continues its busy week with a 4 p.m. non-league home game versus Mount Aloysius Thursday.