Neil Redfearn's Blades were pegged back by a last-minute penalty against Leicester City, but came from behind in the second half to lead 2-1 amidst a share of the points.
Returning to the Technique Stadium for the first time in seven months, United fell behind inside two minutes when Millie Farrow tapped home from close range.
While it was far from the ideal start against a full-time professional outfit, the Blades fought back in style and controlled large parts of the first half.
Sophie Walton went closest when her looping effort came off the crossbar, before Mel Johnson scored her first for the club and her first of the afternoon with a brilliant effort from range.
It gave United the momentum to build on at the start of the second half and the hosts took the lead when Johnson was well placed to tap home after Jade Pennock's effort had been pushed away.
Both sides gave it everything in what became a match of attrition, both teams knowing how important the points could be despite being early days in the campaign.
United couldn't really find a chance to seal it as Leicester pinned them back looking for an equaliser, but the centre-back pairing of Leandra Little and Ellie Wilson repelled everything the Foxes threw at them.
But the visitors got their point in the dying minutes when debutant Hannah Coan was adjudged to have fouled Flint inside the box, the Leicester striker picking herself up to fire home past Kitching for a share of the points.
"I'm super proud of them," said head coach Neil Redfearn. "They battled, they fought and I thought we deserved to win. They're full-time, we were hanging on a little bit but there wasn't much in it. You're looking at a good performance today. I thought we were magnificent today. Everyone will beat one another, all we can do is concentrate on ourselves and make sure the level is good and it was good today."
Blades: Kitching, Wilson, Little, Hartley, Lipka (Lord-Mears 72), Pennock, Wilkinson (Matthews 88), Dixon, Walton, Sarri (Coan 67), M. Johnson.
Unused subs: Batty, Docherty, A. Johnson.