But they were made to struggle in the first half by a battling Bradford side slipping deeper into relegation trouble.
Player-manager David Wetherall marshalled his defensive forces to keep Scunthorpe at bay as the home side dominated much of the opening 45 minutes.
But only once was goalkeeper Donovan Ricketts really tested when he kept out a shot from Sharp.
City might even have snatched a shock lead with Billy Paynter going close with a far post header.
It was Scunthorpe who went in front in the 56th minute when leading marksman Sharp netted his 27th goal of the season after twisting in the box to fire in a close range shot that was deflected past Ricketts.
Bradford rallied and thought they were back on level terms in the 65th minute when Weatherall headed home from a corner.
But their joy was short-lived when referee Clive Oliver ruled out the effort for a foul on goalkeeper Joe Murphy.
It was Scunthorpe who struck again in the 76th minute when Beckford made it 2-0 with his seventh goal in 12 games since joining the club on loan from Leeds.
He found the bottom corner of the net with a speculative left-foot drive from 25 yards that left Ricketts no chance.
It means Scunthorpe march on at the top, while Bradford still have real problems in the relegation zone after an 11th away defeat.