The veteran striker overtook David Nugent’s record total in the second tier since it was rebranded in 2004 and kept the Blades in the hunt for a play-off spot.
It was a typical poacher’s goal for the visitors’ captain as he swooped on a loose ball in the penalty area to earn his side a deserved victory and keep their opponents in the relegation places after a largely one-sided encounter.
The win was capped off late on by an own goal from Callum Morton.
Heckingbottom said: “It was a really strong performance and well deserved.
“We had to be patient, we spoke about that before the game, and we started strongly. We were good in possession and strong at set-plays. We had to wait a while to get that goal but I don’t think anyone can say it wasn’t deserved, or the second either.
“We had 15-20 shots and we just needed that little bit of composure in and around the box and that’s what Billy gave us when the ball dropped to him.
“It’s about his hunger. He trains hard, looks after himself, responds to getting pushed and has a hunger to score goals.
“That record will mean a hell of a lot to him. He is trying to squeeze every little bit out of his legs and body for as long as he possibly can to score goals in what is a really difficult league.”
Sharp struck on 54 minutes, swooping on a loose ball after home defender Nathan Thompson had miscontrolled an Oliver Norwood ball into the area.
It was no more than the Blades had deserved after Jayden Bogle and John Egan had both missed good chances, the latter heading over unmarked following a short corner.
Sharp was denied by Steven Benda from another good chance but on 81 minutes Chris Basham headed a corner back across goal, with the ball hitting Morton before going in.
Manager Darren Ferguson said: “It was a game that was always going to be difficult for us. We’ve got to find a way of stopping these sloppy goals.”
Peterborough United: Benda, Kent, Thompson, Knight, Mumba, Fuchs, Grant (Randall 79), Tomlinson (Ward 65), Poku, Clarke-Harris, Marriott (Morton 65). Unused substitutes: Szmodics, Cornell, Jade-Jones, Barker.
Sheffield United: Foderingham, Basham, Egan, Robinson, Bogle, Norwood, Hourihane, Norrington-Davies, Ndiaye (Fleck 71), Brewster (McGoldrick 22), Sharp (McBurnie 79). Unused substitutes: A Davies, Baldock, Berge, Gordon.
Referee: D Whitestone (Northamptonshire).