A disciplined defensive performance deservedly earned them a point and they have now gone nearly 500 minutes without conceding a goal.
In a defence dominated game there were few chances at either end. Scunthorpe might have snatched an early lead when an angled drive from Paul Hayes was turned away at his near post by goalkeeper Marton Fulop.
It was not until just before half-time that Scunthorpe chiselled out another opening, when leading marksman Martin Paterson found himself free on the edge of the six-yard box, but headed over from a free-kick.
At the opposite end the Foxes could not even muster a single shot at goal throughout the entire first half.
Their first attempt finally came in the 48th minute when striker Matt Fryatt headed well wide.
City had a setback in the 61st minute when Hume, who had already been cautioned in the first half, received his marching orders for a second caution following a challenge on Scunthorpe full-back Cliff Byrne.
That though seemed to stir City into action and they thought they had snatched the lead in the 68th minute when centre-back Patrick Kisnorbo headed home a free-kick from Alan Sheehan, only to see it ruled out for offside.
Sixty seconds later they had the best chance of the game when Fryatt pounced on a mistake by home skipper Andy Crosby to break free into the box, but his shot was blocked by the legs of goalkeeper Joe Murphy.
The Iron, who had been beaten in both their previous home games, tried to search for a breakthrough in the closing minutes, but never threatened a winner as Leicester closed ranks in front of goalkeeper Fulop.