Town took a first-minute lead when captain Tom Lockyer netted with just 38 seconds on the clock at the Coventry Building Society Arena, but saw their advantage wiped out in the final seconds of the first half when Matty Godden slammed in a penalty.
Manager Rob Edwards made two changes from the side that beat Stoke last week in the Town's last league outing, Marvelous Nakamba makes his first start for the club after coming off the bench against Stoke City last weekend.
Gabe Osho kept his place in defence following the midweek defeat at Grimsby Town as Cody Drameh missed out after picking up a knock in training.
Midfielder Henri Lansbury made a welcome return to the matchday squad - back on the bench for the first time since sustaining an injury against Sunderland in October - while Joe Taylor was also named among the substitutes for the second time since joining in the January transfer window.
Town made a dream start with Lockyer netting after just 38 seconds. Douugty took a short throw to Clark, got the ball back and beat his man before curling in a cross that deflected off Coventry's Kasey Palmer's outstretched boot and Reece Burke's head before Wales international Lockyer steered home left-footed.
Both sides had penalty appeals turned down inside the opening ten minutes before City striker Viktor Gyokeres drew a flying save out of Horvath, and Kyle McFadzean - who had appeared to impede Adebayo as he made his way into the Sky Blues' box moments earlier - shot just wide from the corner that followed.
Adebayo met Doughty's right-wing corner with a firm header, straight into keeper Ben Wilson's hands, in the 17th minute before the right wing-back skipped to the right byline again and cut back, only for Coventry to clear.
Bell was soon raiding down the other flank and sent a dangerous-looking cross-shot in that Wilson did well to hold at his near post, before gatherin again as Bell picked out Adebayo for a near-post header that was straight at the home keeper.
Town were increasing the pressure at this stage, Wilson having to push an inswinging Doughty corner over his bar before Mpanzu saw a piledriver from the edge of the box blocked.
Burke had his name taken by referee Stephen Martin for a foul on Gyokeres as half-time approached, then Coventry were handed their route back into the game as Osho dragged the Coventry striker down as he looked to finish a low cross from Godden in the 45th minute.
Osho was shown yellow, then Godden stepped up and slammed the ball past Horvath from 12 yards to send the sides in level at the break.
Coventry centre-back Luke McNally went on a rampaging run from inside his own half to hit a low shot that had Horvath diving low to his left to save two minutes into the second half, but Bell and Doughty were soon flying down the Town flanks again, Bell's cross evading everyone before Doughty hit the outside of a post with his attempt after retrieving the ball on the right.
Morris sent a glancing header just over the bar from another Doughty centre just before the hour, then Coventry were denied by the woodwork as Palmer's curling effort came back off the crossbar.
A quick free-kick between Clark and Doughty set the latter racing onto the ball to deliver another testing cross, which Lockyer headed back into the six-yard box but Coventry cleared, with Bell then booked for another foul on Gyokeres.
It was Doughty's last action, with the wing-back receiving treatment and then being replaced in the 65th minute by Fred Onyedinma.
Osho made a crucial 74th-minute block to deflect a Gyokeres effort wide of the target, then Cauley Woodrow - on as a sub for Adebayo - saw a header from a Morris cross pushed away by a flying Wilson.
From the corner, the former Barnsley man then found himself unmarked at the far post, only for Callum Doyle to throw his body in the way and divert for another set piece.
The hosts were reduced to ten men with five minutes left when Josh Wilson-Esbrand saw red for a foul on Onyedinma that sparked a melee that also resulted in yellow cards for Morris and Coventry captain McFadzean.
Edwards withdrew Clark and threw another attacker into the fray, handing Taylor his debut, but the Hatters couldn't find a way through the hosts' backline and had to settle for a point that maintains their fourth place in the Championship table ahead of Wednesday's trip to Preston.
Goals:
LT - Lockyer 1
CC - Godden (pen) 45+1
Att: 20,366 (2,843)