It is the club's most successful season to date, with Dean Davenport's side level with third-place Bristol City but for goal difference.
Goals from Charley Clifford and Sophie McLean completed a comeback against United comeback to secure the 2-2 draw.
United got off to a near-perfect start, as Lucy Watson’s low cross in the box found Courtney Sweetman-Kirk in the box, but her shot fell wide of the post.
The Blades were the more dominant side as they continued to challenge Palace, and their chances eventually paid off in just the 10th-minute. Rhema Lord-Mears’ long-range strike flew into the top corner to put the home side in front.
Goalkeeper Emily Orman kept Palace in the game by stopping Sweetman-Kirk’s low range shot, preventing United from doubling their lead. It was just as well, as Palace had it all to play for on Sunday afternoon: victory and the correct combination of results elsewhere could have pushed them to second.