Cliff Byrne, Andy Butler, Lee Ridley, Ian Baraclough and Steve Torpey came into the side as manager Brian Laws shuffled his pack.
Trialist Derek Asamoah, who arrived at the club on Monday after Doncaster opted against offering him a contract, was on the bench.
Leeds' Norwegian midfielder Eirik Bakke created the first chance of the game, seeing an effort come crashing back off a post with just seven minutes on the clock.
United's first choice came with 35 minutes gone, with Andy Keogh firing over then seeing a last-ditch tackle prevent a shooting opportunity.
Goalkeeper Joe Murphy was replaced before the break as a precaution, but his thigh injury is not likely to keep him out of Saturday's friendly with Sheffield United.
Youngster Josh Lillis came on to replace him, making his first senior appearance at Glanford Park.
But his first action was to pick the ball out of his own net, when Robbie Blake poked the ball past him.
United immediately levelled through Matty Sparrow, who turned the ball in from close range following good work from Andy Keogh - playing against his former club - and Dave Mulligan.
And Sharp scored the winner after 53 minutes, when he headed home from a corner.
Neither side looked like adding to the scoreline, but Scunthorpe were dealt a major blow when Andy Butler was stretchered off with a shoulder injury.