The lively Kike hammered a powerful shot into the side-netting midway through the first half as the Championship side continued to threaten, before Baptiste was stretchered off with a nasty-looking injury and replaced by Andre Bennett.
York barely threatened until just after half-hour mark, but when they did it was only Dael Fry's goal-line clearance that kept the scores level.
Husband then struck the post just before half time, but the second half began at a much slower pace than the first.
There was little goalmouth action until George Friend sent a shot flying over the top of goal in the final 20 minutes.
However, just as the game appeared to be headed for a goalless draw, England Under-19 international Fewster popped up with a goal 11 minutes from time to seal victory for Aitor Karanka's side.