Although the visitors struck the woodwork twice, they had to rely on a superb performance from their goalkeeper Adriano Basso to keep their goal intact.
There were chances at both ends within the first minute with Lee Hendrie forcing Basso into a fine save, before Gareth McAuley raced across to block Darren Byfield's shot.
Basso then needed two attempts to smother Dudley Campbell's drive which was quickly followed by Jamie McCombe diverting Iain Hume's shot into the side-netting.
Paul Henderson saved well from Michael McIndoe, before McAuley deflected Byfield's shot for a corner as the frantic pace continued.
Midway through the first half, Kelvin Etuhu blazed over, before the same player's swirling cross struck the roof of the net as the home side's bright start showed no sign of abating.
Leicester squandered a magnificent opportunity on 36 minutes when Hume robbed Lee Johnson only to drive wide from 15 yards with just the keeper to beat.
Another chance for the home side followed quickly with Hume shooting just over after Campbell had stepped over the ball following Etuhu's surging run.
On the stroke of half-time, Basso was at full stretch to palm away Hume's close-range effort with Etuhu's follow-up drifting wide.
It was the visitors who came closest to scoring on 52 minutes when Marvin Elliott's angled shot beat Henderson before rebounding off the base of the far post and into the arms of the grateful keeper.
Then on 63 minutes, the Leicester woodwork was rattled again when Brian Wilson crashed a 30-yard drive against the underside of the bar with the ball bouncing on the line where it was pounced on by Henderson.
Yet another chance came the home side's way on 75 minutes when Hendrie's low cross evaded everyone until reaching Joe Mattock at the far post with the teenage substitute side-footing wide from close range.
Another substitute, Barry Hayles, tangled with Liam Fontaine inside the area before tumbling and having his penalty claim turned down.
Basso came to his side's rescue yet again to pull off excellent saves in quick succession to deny Matty Fryatt and then Mattock.
In time added on, City substitute Ivan Sproule broke clear but Henderson was alert to his near post drive.
Then right at the death, Steven Howard's drive from a Hendrie corner appeared goalbound until Basso was there once more with another splendid save.