Jade Pennock scored a second 90th minute winner in as many games to ensure United's women's team ended March with a 100% league record.
The Blades trailed to Hayley James' header with little over 15 minutes to go but a stunner from substitute Ellie Gilliatt set up another dramatic finale one week on from the win at Tottenham.
It had been a frustrating match for the Blades up to that point as chances were few and far between despite Carla Ward's side being in relative control of the encounter.
Ebony Salmon was once again lively up front and the on loan forward fired over the first opening as United looked to take the initiative.
Pennock saw two efforts from distance well held by Demi Lambourne while Fran Bentley was only called into action to save a header as Leicester tried to build some momentum.
The Foxes should have taken the lead immediately after the break. Half-time substitute Sam Tierney doing brilliantly to stop Mel Johnson rolling the ball into an empty net after the striker used her pace to round Bentley.
Salmon lobbed an effort wide as United pushed for a winner but they were dealt a blow with 15 minutes to go when Hayley James headed home Rosie Axten's corner.
Not to be deterred, the Blades hit back with immediate effect. Super sub Gilliatt picked the ball up outside the box and fired an unstoppable effort into the top corner for the equaliser.
Salmon hit the post with a stinging effort before she was denied by Lambourne as the game entered the stoppage time.
It didn't matter though, the corner turned in by Pennock who scored her second last-gasp winner in as many games and sealed another vital three points for United.
Blades: Bentley, S. Barker, Pennock, Cox, Rayner (Sarri 88), Paul, Dixon, H. Barker, Cusack, Hartley, Salmon.
Unused: Davies, Ford, Housley.