Marcus Bent's late strike snatched a point for Leicester after Wayne Rooney appeared to have spoiled Paul Dickov's return to the Foxes line-up.
Alessandro Pistone and Nikos Dabizas went close before Bent had a goal disallowed for handball.
Everton striker Duncan Ferguson was then shown two yellow cards for clashes with Dabizas and Steffen Freund.
Rooney appeared to have won it when he got on the end of a long ball before Bent pounced from a last-minute corner.
The game kicked off after a show of support from the Leicester fans for the trio of players charged with sexual aggression in Spain but only one of those - Dickov - was in the starting line-up.
Everton carved out the first opening when Pistone forced Ian Walker into a smart save with a 20-yard drive.
But the home side could have taken the lead when a Muzzy Izzet free-kick from the right found Dabizas, only for his header to go over.
With the strong winds making making life difficult for both teams, there were precious few moments of quality, although Dickov turned smartly and fired just wide and Rooney blazed over at the other end.
There was controversy just before the break when Bent headed against the bar from an Izzet corner and when the rebound went in off him, referee Barry Knight ruled that it had hit his arm.
30 mins: Bent has goal disallowed
41 mins: Ferguson is sent off
75 mins: Rooney scores for Everton
90 mins: Bent levels for Leicester
Knight was at the centre of another row minutes later when he gave the big striker his marching orders.
Ferguson had been booked for catching Dabizas in the face with his arm, and then Knight cautioned the big Scot for wrestling Freund to the ground.
Ferguson appeared to gesture to the Leicester supporters as he went off.
In the second half Everton were content to sit back and City struggled to make their numerical advantage tell.
Pistone almost turned an Izzet cross past his own goalkeeper Nigel Martyn but there were few other moments of excitement for the Leicester fans.
And it got worse for the Foxes when Rooney - who turned the game between these teams in December - did the damage again.
After failing to connect with a good Steve Watson pass 10 minutes earlier, Rooney made no mistake when Radzinki set him up.
Everton's defence stood firm in the closing minutes as Leicester desperately tried to snatch a point to boost their survival chances.
The visitors might even have added to their tally as Thomas Gravesen went close after a fine solo run.
Just when it looked like it was all over for City, Bent netted from a corner which had followed a tremendous Martyn save to deny Riccardo Scimeca's 18-yard drive.
Leicester: Walker, Scimeca, Dabizas, Heath, Thatcher, Bent,
Freund (Nalis 84), Izzet, Benjamin (Guppy 45), Dickov,
Ferdinand (Canero 57). Subs not used: Coyne, Davidson.
Everton: Martyn, Watson, Stubbs, Yobo, Pistone,
McFadden (Radzinski 45), Gravesen, Linderoth, Naysmith,
Rooney (Campbell 88), Ferguson. Subs not used: Wright, Unsworth, Nyarko.
Sent off: Ferguson (41).
Booked: McFadden, Ferguson, Gravesen, Radzinski, Rooney.
Referee: B Knight (Kent).