As the ball bobbled in the area Sharp controlled, swivelled and rifled a powerful low drive past Donovan Ricketts.
Bradford had the better of the opening exchanges, but a lacklustre second-half showing left them a without a win in their last four matches.
Recalled striker Eddie Johnson wasted a golden opportunity to put his side in front just three minutes in.
Jermaine Johnson produced the first of a number of dazzling runs, beating two men on his way to the byline. His pull back found his namesake in space eight yards out, but the striker scuffed his shot too close to Joe Murphy.
Six minutes later it was Scunthorpe's turn to be wasteful in front of goal after Sharp sprung the offside trap.
He expertly chipped the ball over the on-rushing Ricketts, neatly controlled it on his chest, and was about to slide the ball in until Marc Bower came to the rescue with a timely challenge.
Both sides were looking to get forward but neither goalkeeper was called upon to make a save until just before the half-time whistle.
Both Sharp and Ian Baraclough forced Ricketts to make acrobatic blocks before the Iron's former Bradford striker, Steve Torpey, had an effort ruled out for a push.
There was just time for Bradford's leading scorer Dean Windass to sting the fingers of Murphy before the interval.
After the break both sides failed to show the fluency they had in the opening period and chances were at a premium.
With little under 15 minutes left, Bradford finally forced Murphy into a save when Lee Holmes burst into the box.
His low effort looked destined for the bottom coroner, but Murphy stretched out a solid left hand to divert the ball to safety and keep the scores level.
After Sharp's strike had given the visitors the lead, City poured forward in a desperate bid for an equaliser but United's defence, superbly marshalled by skipper Andy Crosby, kept them out.