The Blades, who secured their place in the semi-finals of the FA Cup at the weekend, were on top for most of the game and Carlisle had goalkeeper Jordan Pickford to thank for saving them from a heavier defeat.
Pickford was called into action inside the opening minute of the match, keeping out Jamie Murphy's low, angled shot.
Stefan Scougall then shot straight at the Carlisle goalkeeper while Baxter put an effort wide.
Scougall had another chance when he was through on goal, but his shot was saved by Pickford with his legs.
The goal came in the 28th minute when Conor Coady's driven pass found Baxter in the area and he composed himself before putting a low shot just inside Pickford's left-hand post.
Carlisle's best spell came in the latter stages of the game. David Amoo's header was cleared off the goalline by Ben Davies, while Brad Potts and David Symington had efforts deflected wide.