Scunthorpe had the first chance, with Marc Joseph conceding a free kick just outside the area in the opening minutes. Kevin Sharp stepped up to take it but it came to nothing.
But City began to dominate, and after seven minutes a header from Stuart Elliott was tipped over by Tom Evans, and from the corner a shot from Jon Walters nearly found Jason Price a few yards out but Sharp cleared off the line.
After 11 minutes Damien Delaney was adjudged to have handled the ball just outside the area. Sharp's resulting free kick cannoned off the crossbar and into the arms of a grateful Boaz Myhill.
City deservedly took the lead after Walters won possession about 20 yards out and slipped the ball through to Ben Burgess, who timed an exquisite chip over Evans from the edge of the area.
City, buoyed up by the goal, were causing problems in Scunthorpe's defence, though Cliff Byrne was keeping them at bay with a few last ditch tackles.
After 20 minutes, a swerving 20 yard shot from Taylor was tipped over by Myhill, but ten minutes later City had extended their lead.
Elliott on the left wing did well to beat Byrne and put in a cross to Burgess who scored with an excellent low diving header from about 10 yards.
The second half was much more low key and slower paced, with Scunthorpe inevitably looking more organised and having the greater share of possession.
After 65 minutes, Walters missed a great chance to go three up when, with only the keeper to beat, he chipped well over the bar.
Three minutes later Steve Torpey, who was already on a yellow card, seemed to strike Price in the box, and was lucky to stay on the field.
But it was 'game on' after 73 minutes when Steve MacLean grabbed one back for the Iron after Myhill failed to hold on to a shot and no City players were there to put out the rebound.
Five minutes later, Groves shot well wide after a period of intense pressure on City's box by Scunthorpe.
Two minutes from time, substitute Allsopp hit the post after running clear of the defence and the ball rebounded into the arms of Evans.
A hectic last few minutes ensued, but in the end City were well worth the victory.