Goals from Michael Doyle and Dave Kitson were enough to edge out the hposts, who grabbed a late reply through Stephen McGinn, giving the Blades their first double of the campaign.
Overall, it was a dominant display by the visitors, particularly after the break when their pressure began to tell.
Several opportunities to break the deadlock had been missed when, in the 63rd minute, the Blades benefitted from a touch of luck with their opener.
Jamie Murphy made ground down the left before finding Jonathan Forte whose effort was saved, only for the subsequent clearance to hit Doyle and bounce into the net. The goal was slightly marred when Doyle was booked for his celebrations.
A patient build-up resulted in United doubling their lead through Kitson in the 72nd minute, the experienced striker blasting in from 25 yards before goalkeeper Chris Weale could even move.
Forte almost made it 3-0 until, at the other end, McGinn’s 35-yard free-kick ensured there were some nervous moments for the visitors before they could celebrate their first win of the year to move back up to fifth in the table.