A Michael Higdon header gave Crewe the lead before Iain Hume levelled after Alan Sheehan had been sent off for two yellow cards.
City went close on seven minutes when Ross Turnbull parried Johannes Gudjonsson's 18-yard drive on to the bar and out for a corner.
Then a ricochet was seized upon by Elvis Hammond who rounded Chris McCready before firing in a 12-yard shot which Turnbull turned away.
The home side continued to press and were close again on 20 minutes when Gudjonsson fired in a shot from 10 yards which Turnbull blocked.
The Foxes thought they had broken through when Hammond had the ball in the net after Turnbull had blocked Gudjonsson's long-range effort, but the former Fulham striker was flagged offside.
Crewe's only threat had been the pace of Steve Jones but they created a clear chance on 35 minutes when the home rearguard failed to cut out Kenny Lunt's cross to the far post. The ball dropped for Higdon who drove a close-range angled shot over the bar.
That should have set alarm bells ringing among the Leicester defenders but they were still dozing five minutes from the break when Crewe took a surprise lead.
Jones was allowed to get in a right-wing cross which drifted unopposed to the far post where Higdon made no mistake to squeeze home a header from three yards out.
City dominated after the break but they were reduced to 10 men on 57 minutes when Sheehan was sent off. His first yellow card had been for handball and he was shown a second for a foul on Billy Jones.
But on 65 minutes Leicester levelled when Hume gathered a Gudjonsson pass and hammered an angled eight-yard drive into the far corner of the net.
Hume continued to be City's best player and Turnbull had to be at his best to claw away the striker's brilliant 25-yard drive.
Stephen Hughes came on as a late substitute and his initial contributions were vital as he cleared shots off the line from Gary Roberts and then Jones in quick succession.
But it was Leicester who finished on top but frustratingly for the home support failed to find a winner that their dominance deserved.