On a day of family-based events, including a mothers vs. daughters match in Quorn, City's women also announced the signing of forward Simran Jhamat from Liverpool.
Inside the opening 10 minutes, Ebony Salmon went close for the visitors, while Foxes goalkeeper Demi Lambourne did well to save from Jade Pennock shortly after.
Leicester were denied an opener after the interval when Melissa Johnson rounded United's 'keeper, but a late block on the line kept the scores level.
With 17 minutes to go, though, the home side were in front as Hayley James headed home, sparking jubilant celebrations from a healthy home crowd in Quorn.
However, just three minutes later, the Blades drew level through Ellie Gilliatt and, with one minute to play, Pennock won it for the Yorkshire outfit.
Leicester are now eighth in the 11-team league standings, while they next welcome Durham Women to Farley Way on Sunday 28 April (2pm BST kick-off).
City: Lambourne, Franklin-Fraiture, Jackson, Morgan (c), Domingo (Axten 64'), M Johnson, Ayisi, Brown, N. Johnson, Smith, Jhamat (James 59')
Subs not used: Charlton, Nymoen, Worts, Moncaster
Goal: James 73'
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