United's women's team were denied a fourth win in five by a resolute Millwall side, Sophie Jones' equaliser in the second half ensuring a split of the points after falling behind.
It turned out to be a frustrating day for Carla Ward's side who did more than enough to win the game but couldn't breakdown Millwall in the final half an hour.
Tania Marsden had the perfect chance to put United in front early on but the striker, making her first Championship start of the season, fired wide after Riva Casley's slip gave her a clear sight of goal.
United pressured but could only create half chances before the hosts took the lead shortly before half-time.
A corner from the left was headed home by Priest, the ball finding the corner and leaving Alex Brooks with no chance.
Millwall should have doubled their advantage when Evie Clarke failed to control the ball in front of goal and Izzy Ford went close to an equaliser when her effort was deflected agonisingly wide just before the break.
United though did find the equaliser 10 minutes into the second half after a cross from Ford into the box was scooped back across goal by Veatriki Sarri and fired home by Jones after her initial header had been saved.
It gave the Blades the momentum to dominate the final half an hour of the match but the winner never came.
Substitute Chloe Dixon saw several efforts blocked, as did midfielder Sam Tierney but Millwall's defence stood firm under intense pressure.
Sarri went close with a curling effort from the edge pf the box but the breakthrough never came and United had to settle for a point.
Blades: Brooks, Pennock, Cox, Ibbotson, Gilliatt, Tierney, S. Barker, Ford (Dixon 57), Sarri, Jones, Marsden (Paul 46).
Unused subs: Davies.