.Gilberto Silva struck on the hour mark for Arsenal who then had Ashley Cole sent off for a violent tackle before never say die Leicester were finally rewarded with an equaliser in the third minute of time added on.
City's danger from set pieces was clear early on when James Scowcroft headed Riccardo Scimeca's free-kick just wide of the far post.
Arsenal responded with Freddie Ljungberg's lofted ball putting through Jeremie Aliadiere in the 14th minute, but Ian Walker was well placed to gather the striker's weak shot.
City's willingness to scrap for every ball meant Arsenal struggled to establish rhythm while in defence the visitors had to be vigilant against Leicester's tactics of hitting early balls to front men Les Ferdinand and Marcus Bent.
Chances were at a premium in the first half with Davidson's 25-yard shot on 35 minutes almost catching out the keeper, but the ball drifted just wide.
Arsenal started the second half in more lively fashion with Walker spectacularly clawing away Gilberto's 25-yard swerving drive.
City then had a strong penalty claim waved aside after Sol Cambell appeared to tug Bent's shirt inside the box, but the Gunners found themselves ahead on 60 minutes with a trademark breakaway goal.
The ball was moved quickly from the keeper to Robert Pires and a mistake by Ben Thatcher allowed Dennis Bergkamp to turn inside and cross for Gilberto to score with a thumping header.
Five minutes later Arsenal almost doubled their lead when Bergkamp's free-kick was flicked goalward by Gilberto, but Walker intervened to push the ball on to the post.
The Gunners were reduced to ten men with 18 minutes left when Cole was shown a straight red card after he had slid in and caught Thatcher with a two-footed lunge.
Thereafter City laid siege to the Arsenal goal with sub Paul Dickov going close when his angled shot to the near post almost deceived Jens Lehmann.
But City kept plugging away and finally got their reward with almost the last kick of the game when Impey's long ball into the box was headed down and across the goal for sub Craig Hignett to bundle home from close range.