In the battle of promoted sides, it was the visitors who started brighter, as Stephy Mavididi - who scored in this fixture last season - was not as precise this time, scuffing his effort from just a few yards out. Abdul Fatawu then curled a fine shot towards the far corner of the net, but Arijanet Muric pushed the ball away.
Facundo Buonanotte tested Muric after driving to the edge of the box, before Ipswich started to grow into the game.
Dara O’Shea should have directed his header better at the back post after it bounced off the surface and over the bar, as the hosts continued to grow in momentum, but Conor Chaplin struck just wide after cutting inside, as the contest stayed goalless going into the second half.
It did not take too long for the opening goal to come, as Leif Davis - on his 100th Ipswich appearance - produced a magnificent side-footed volley into the bottom corner after he was picked out by Sam Morsy.
Harry Winks tried to instantly respond for the visitors, but his left-footed strike was parried away by Muric.
Ipswich’s task to hold onto victory got harder when Kalvin Phillips was dismissed for a second bookable offence, with 13 minutes plus stoppage time still left on the clock.
The Tractor Boys had dropped 10 points from winning positions already this season, and unfortunately for them, the inevitable happened again.
Ayew, who netted late last weekend, poked home an equaliser for Leicester in injury time, in a result that keeps Ipswich in the relegation zone, and sees the visitors pick up seven points from their last four PL matches.
Flashscore Man of the Match: Leif Davis (Ipswich Town)