Rory Fallon's first goal for Town wasn't enough to give Blues the points against the 10 men of Coventry.
The New Zealand international gave Town a deserved lead at the break with a close range finish after Jack Colback had been denied by Keiren Westwood.
Carlos Edwards had already hit the bar before the opener as Blues created the better chances throughout the 90 minutes.
Freddy Eastwood levelled the scores early in the second-half but the Sky Blues played the last half hour with 10 men after Marlon King was dismissed for a foul on Darren O'Dea.
Roy Keane made four changes to the side that beat Leicester in Town's last game, the 3-0 win over Leicester two weeks ago.
Jaime Peters came in for his first League start since October to replace loanee Gianni Zuiverloon, who returned to West Brom in midweek while O'Dea was restored to the starting line-up.
Carlos Edwards washanded a start in place of the injured Shane O'Connor while the final change saw the welcome return of Gareth McAuley, who was back in action for the first time in two months following an achilles operation and the Northern Ireland international showed a cool head to deal with a long ball aimed at King in the first five minutes.
Town had the first incisive move of the match though when David Norris exchanged passes with Fallon, his cross cleared three yards out by James McPake.
Marton Fulop fisted away from King's dangerous cross while his counterpart, Westwood had to be quick off his line to cut out the danger as Jason Scotland looked to get on the end of Fallon's header.
Eastwood fired wide after O'Dea gave the ball away but it was Town who carried the main threat in the first-half and Fallon had a chance to open the scoring on 20 minutes but he couldn't beat Westwood from Edwards' cross.
King hit the post with a header from David Bell's corner but Edwards went even closer with a 30 yard blockbuster that rebounded back off the underside of the bar via Westwood's glove.
Grant Leadbitter arrowed a shot inches wide as Town turned up the heat on the Coventry goal, while King continued to look the most likely to open the scoring for the Sky Blues - his header comfortably saved by Fulop.
Eastwood had a shot deflected wide before Town got the goal the play deserved three minutes before the break, a neat move involving Norris and Colback saw the Sunderland loanee denied by Westwood's flying left hand but Fallon was on hand to put the ball into the empty net.
Coventry took just three minutes to get back on level terms as the second-half got underway, Eastwood beating Fulop from the edge of the box after King had won the long ball.
Fallon almost set up Norris after a superb cross from Edwards as Town looked to respond before Coventry were reduced to 10 men when King was shown the red card by referee Booth for a foul on O'Dea just before the hour.
Scotland was yellow carded two minutes later after a challenge on Richard Wood, the home crowd agitated that the numbers weren't evened up, the volume turned up louder still when Fulop was judged to have been fouled with the ball loose in the Blues' box.
It took a great tackle by McPake to deny Scotland following Edwards' astute pass, then Colback sent a gilt edged chance wide after Fallon's clever lay-off.
Coventry replaced Bell with Clive Platt for the last 20 minutes, the former Colchester striker was on target in the Sky Blues' 2-1 win at Portman Road in October.
Connor Wickham was introduced for the last 15 minutes, Scotland making way in Town's first change.
Richard Keogh hooked the ball clear from Fallon's header as Town searched for a winner in the closing minutes, Blues adding to the firepower with Ronan Murray on for Colback.
Tommy Smith did brilliantly to deny Platt at the far post as he looked likely to head in, Troy Brown handed the last five minutes, Peters, who took a knock, making way.
Eastwood was replaced by Martin Cranie in the five minutes of added on time but neither team could make the additional play count, McPake's header from Lee Carsley's free-kick giving Town one final anxious moment.
Coventry: Westwood, Keogh, McPake, Cameron, Wood, Bell (Platt 70), Carsley, Doyle, Eastwood (Cranie 89), King, Jutkiewicz. Subs not used: Ireland, O'Halloran, O'Donovan, Thomas, Baker. Sent-off: King.
Town: Fulop, Peters (Brown 86), McAuley, Smith, O'Dea, Edwards, Norris, Leadbitter, Colback (Murray 84), Fallon, Scotland (Wickham 75). Subs not used: Lee-Barrett, Delaney, Livermore, Kennedy. Booked: Scotland.