It was not a classic by any means because of the conditions but Chesterfield could not make the most of long periods of possession and created few openings against a Scunthorpe back four in which Steve Foster was outstanding.
The visitors had few chances themselves but Sharp made one count when he was first to react when Barry Roche was unable to hold Matthew Sparrow's low shot.
The ball bounced away from Roche and Sharp tapped the rebound in from six yards for his seventh goal of the season.
Scunthorpe played some flowing football in the opening 20 minutes and Cleveland Taylor would have been through on goal if his control had been better when Sharp picked him out with a clever pass in the 20th minute.
But Chesterfield gradually took control of the midfield and Joe Murphy had to be at his sharpest to get down to his right to block a low shot from Mark Allott in the 32nd minute.
But Chesterfield's final ball lacked quality and Scunthorpe were able to clear their lines for most of the game without ever really being stretched. In fact the better chances fell to the visitors and Taylor should have given his team a more comfortable cushion to defend in the 56th minute.
Marcus Williams played a superb ball over the defence from the Chesterfield right and Taylor was unmarked at the back post but he sliced his shot wide when he should have found the net.
That could have proved costly and Scunthorpe came close to conceding an equaliser when Richard Hinds made a rare error in the 73rd minute but Chesterfield could not punish them.
Derek Niven pounced on the loose ball and set up Colin Larkin but his 15-yard volley flew straight at Murphy.
Kevan Hurst whipped in some good crosses after that but Scunthorpe held firm and the home side rarely looked capable of getting back into the game.