Kari Arnason had given the visitors the lead in first-half stoppage time but Michael McIndoe got his first goal for the Sky Blues to ensure the points were shared.
Coventry went into the match hoping to make it four wins in a row for the first time since December 2002.
In the opening stages, they looked a good bet to reach that milestone with a number of good moves.
Sammy Clingan was the first to threaten, when he fired a half-volley towards goal but the ball deflected off a defender to take it off course.
Jamie Mackie was the visitors' biggest threat and was denied in the 20th minute by a superb Keiren Westwood save. Mackie broke down the left-hand side of the area and hit a shot towards the top of the net, but Westwood tipped the ball over the bar with one hand.
Carl Baker was a nuisance down the right wing and he nearly set up McIndoe with a cross into the box, but the former Hereford man's header went wide.
The game looked set to be level at the break, but Stephen Wright's foul 30 yards out gave the visitors the opportunity they needed. Damien Johnson lifted the ball into the crowded box and Arnason headed past Westwood.
Chris Coleman's half-time team talk must have worked because City pulled level after four minutes of the restart. The chance came through Baker, who sent a ball towards the six-yard area. Substitute Gary Deegan missed the chance to shoot from close range, but McIndoe was waiting behind him to score his first goal for the club.
Coventry pushed on in search of the win and Jon Stead was causing trouble against the Pilgrims. Keeper David Stockdale had to be at solid to stop a powerful 56th-minute shot but was powerless in the 73rd when Stead smashed a shot across goal and past him, but the outstretched boot of McIndoe just missed an easy goal.
The Sky Blues piled on the pressure towards the end but Stockdale and his defence warded off the late threat to hold on.