Leicester had penalty appeals waved aside on 15 minutes when Alex Bruce handled an Andy King header inside his own six-yard area.
Chris Weale was called into action on 23 minutes to tip over a Jonathan Walters header from Bruce's cross.
The Foxes went close to equalising on 28 minutes when Steve Howard's header beat the keeper only for defender Grant Leadbitter, who was standing on the line, to head the ball against his own crossbar.
Weale was then at full stretch to keep out a Gareth McAuley header before City levelled on 38 minutes through Howard.
Lloyd Dyer cut in from the right and his pass ricocheted off Damien Delaney into the path of Howard who, from ten yards out, reacted sharply to poke the ball beyond Arran Lee-Barrett.
Shortly after the restart the Ipswich keeper again denied City, this time saving instinctively with his shoulder to keep out Matty Fryatt's close-range drive.
It proved to be the closest either side came to scoring in the second half with Walters planting a free header wide and Howard rifling a shot over as defences dominated.