Oaklan Buck had put the visitors ahead four minutes before half time with his second goal in two games since signing but Francois Allen equalised on 55 minutes after being set up by Joe Miluk.
However Baker's penalty, awarded after a foul by Warminster sub Jack Miluk, gave Jon Toy's men all three points, a win that sees Sutton move up to tenth place in the early Division One table. Next up will be Calne Town who visit Lakeview on Tuesday night, kick off at 7.30pm.