The experienced marksman headed home Andy Drury's cross in the 95th minute to settle a thrilling encounter, just days after rock-bottom City - who have now thrown away a possible 20 points from winning positions this season - were undone 2-1 late on at Blackpool.
Jay Emmanuel-Thomas deservedly put Town in front midway through the first half, only for Sky Blues skipper Sammy Clingan to level from the penalty spot before fellow midfielder Gary Deegan turned the game on its head on the stroke of half-time to put the hosts 2-1 ahead.
Coventry had not come from behind to win a game all season and their wait was extended just after the hour mark as Richard Keogh brought down Lee Martin, who saw his spot-kick parried by Joe Murphy only for Chopra to convert the rebound.
Chopra then earned his side the points with that late winner.
An unchanged Ipswich XI - desperate to avoid a fourth successive away league defeat - went into the game full of confidence following their midweek 5-1 rout of high-flying West Ham, a first win in seven games.
And it was they who enjoyed the better of the opening stages, Daryl Murphy failing to find the target with the best of a handful of chances.
But the visitors did eventually break the deadlock after 22 minutes.
The Sky Blues made a hash of clearing the ball, Jordan Clarke and Richard Wood both at fault, and it was left for Emmanuel-Thomas to fire home via a slight deflection from the edge of the penalty area.
Coventry had only gained four draws from losing positions this season but it did not take them long to level matters.
Gary McSheffrey's free-kick was put into the the net by Keogh but referee Nigel Miller had already blown for handball against Tommy Smith, and Clingan stepped up to send Arran Lee-Barrett the wrong way from 12 yards.
City moved into the ascendancy for the remainder of the half, David Bell going close to a second when his shot was palmed over by Lee-Barrett.
And just as it seemed the encounter would remain level going into the break, Clarke's long throw was flicked on by Clive Platt and Deegan was on hand to convert from 12 yards.
Wood was called upon to make a crucial interception across the face of goal to deny a bright Town side at the start of the second half.
Drury forced a solid parried save from Murphy before Chopra beat the City stopper only to see the ball roll the wrong side of a post.
Yet Chopra was soon left celebrating in the 64th minute.
Keogh was found guilty of a foul in the area on Martin, who saw Murphy push his resulting penalty on to the crossbar but Chopra followed up to send the ball over the line.
Murphy was again on hand to produce a great stop soon after, this time denying Chopra, before Coventry's on-loan striker Alex Nimely was at the centre of an unsuccessful penalty appeal.
Both sides went for victory in what was a thrilling final quarter which flowed from end to end, and it was Chopra who found the latest of finishing touches to clinch the points for Ipswich.