Scunthorpe had the better of the opening exchanges with Paul Reid's deflected effort narrowly missing the target inside two minutes and Akpo Sodje seeing his effort blocked by County goalkeeper Bartosz Bialkowski when he was slipped in by Mark Duffy after nine minutes.
County's best chance of the first half came in the 40th minute when Yoann Arquin somehow headed over at the back post from six yards out.
The Iron nearly went ahead on the hour when former County man Karl Hawley dinked a clever chip inches wide.
But there was nothing clever about Hawley's awful miss a minute later when, after a terrible mix-up between Bialkowski and Haydn Hollis, he missed a near open goal from Sodje's pull back.
Scunthorpe were made to pay when Leacock stroked the ball home from Neal Bishop's knock-down after 81 minutes for the Magpies' winner.