Championship play-off finalists looked on course for a deserved three points when they led through Kyle McFadzean's 47th-minute opener from a near-post corner.
The Gus Hamer-inspired Sky Blues also wasted good chances either side of the City skipper's strike.
But Mark Robins' men were made to pay when Dewsbury-Hall levelled on 77 minutes before being fed by new signing Stephy Mavididi to curl home an 87th-minute winner - and earn victory for new Foxes boss Enzo Maresca, in his first game in charge.
Gustavo Hamer went the closest to opening the scoring with an audacious effort directly from a corner, which almost caught Mads Hermansen out, curling narrowly wide with the ‘keeper back-tracking.
A good move from the back saw the Sky Blues catch the hosts on the break, progressing forward with Ellis Simms, who’s pass to Kasey Palmer was blocked, but the ball would fall to City’s 45 and he went inches away from finding the back of the net from 20 yards out.
At the other end, Leicester’s first chance fell to former Sky Blues man Callum Doyle, who rose highest at the back post, only for him to be denied by Ben Wilson.
Callum Doyle against the club where he spent last season. Hamer, who has had a disrupted pre-season, then crucially came off with a calf injury and, without their main influence, the visitors were made to pay for their profligacy when Dennis Praet crossed from the right for Dewsbury-Hall to power home an equalising header.
Coventry substitute Wright had a chance to put Coventry back in front with a powerful shot deflected onto the bar by Hermansen, but Godden diverted the rebound wide, with the keeper beaten.
And, barely a minute later, Leicester went back up the other end to win it, with Dewsbury-Hall's superb right-foot curler from 15 yards.
Leicester found an equaliser ten minutes from time and it came from Dewsbury-Hall, who rose highest in the area to head past Wilson.
The Sky Blues thought they’d won it five minutes from time, Haji Wright raced through on goal and his strike deflected off Doyle and was saved onto the bar by Hermansen to keep the scores level.
However, it would be the hosts who would snatch it with minutes left on the clock when Dewsbury-Hall fired in his second of the game to claim all three points.
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