Tranmere were a good match for their visitors in the opening period but they fell away later and Iron keeper Joe Murphy did not have a real save to make throughout the 90 minutes.
Steve Davies hit the side-netting early on for Tranmere after a quickly taken free-kick and Paul McLaren struck the outside of a post with a 20-yard effort on 11 minutes.
Sharp lobbed just wide for United and Jermaine Beckford volleyed over.
The Merseysiders had a golden chance in first-half stoppage time but McLaren blazed over after being set up by Davies.
The opening goal for Scunthorpe came from a 55th minute corner. Kevan Hurst delivered the cross, Andy Butler's header was held by home keeper Gavin Ward but he fell over his own line.
Chris Greenacre was just wide from the edge of the box for Tranmere after 61 minutes but Scunthorpe doubled their lead nine minutes later.
Sharp was left with an easy tap-in for his 29th goal of the season from a Beckford pass after good work by Cleveland Taylor.
Taylor produced a man-of-the-match performance for the winners. There was also some excellent work from Hurst and skipper Steve Foster.
McLaren tried hard for Tranmere but they were second best on the day.
Rovers' Calvin Zola collected an unnecessary booking for Tranmere with 14 minutes left and a minute earlier Scunthorpe's Marcus Williams went in to the book for a foul.
Tranmere tried to liven things up when sending on Chris Shuker for the last 25 minutes but he failed to make any real impact.