The home side more than matched their opponents and came back well after the shock of conceding an early goal.
The visitor had made their intentions clear as early as the first minute when Paul Hayes shot flew a foot past the post.
The league pacesetters need not have worried as two minutes later they went in front as Hayes' low cross found Steve Torpey, who had the simple task of tapping home at the far post.
A long injury delay as Ian Baraclough received treatment stemmed the flow of pressure by Scunthorpe and they were hit by a swift break from Chester, who drew level on 19 minutes.
A long ball was won by Michael Branch and Stewart Drummond strode forward and crossed for Kevin Ellison to sidefoot home.
Cleveland Taylor showed good pace down the right flank to create a half chance for himself, but Wayne Brown was well positioned to save.
The Scunthorpe striker then had an appeal for a plenty turned down, when he went down in the box while under pressure from Paul Carden.
Chester was forced into a change as keeper Brown was replaced by Chris MacKenzie on the hour mark and goalscorer Torpey then missed a superb chance, chipping wide with only the keeper to beat.
Chester had their own appeal for a penalty waived away on 76 minutes as Ellison went down under a challenge from Nathan Stanton, the city midfielder earning a yellow card for diving.
It was the home side doing much of the pressing late on and the best chance fell to Ellison who hit a half-volley over the bar from just inside the box.