Rovers and City began the evening in unexpected relegation trouble despite bright starts to their respective campaigns, and Freddy Eastwood's first-half strike looked set to consign Sean O'Driscoll's men to an eighth defeat in their last 12 league games.
The result will go some way towards easing the pressure on under-fire Coventry boss Aidy Boothroyd who would have seen his side leapfrog Doncaster in the table had Hayter not beaten an impressive Michael Quirke before the final whistle.
Coventry had the first chance of the match after six minutes, Gary McSheffrey finding space on the edge of the area to test Gary Woods, who saved comfortably.
The hosts responded through Franck Moussa, the Belgian jinking his way into the Sky Blues' box to launch a low left-footed drive past the hand of outstretched rookie goalkeeper Quirke but wide of the post with 17 minutes played.
Lukas Jutkiewicz could have put Coventry ahead just a minute later, Woods reacting quickly to parry a bullet header over his crossbar.
The visitors did not have to wait much longer to make the breakthrough, McSheffrey tidying up after a deep inswinging corner from David Bell to slide the ball across the six-yard box to a loitering Eastwood.
The former Wolves man slotted his fifth league goal of the season into the top corner to give Coventry the lead after 23 minutes.
Eastwood could have doubled the visitors' advantage immediately after kicking off, drilling right-footed from distance but failing to hit the target.
The hosts had an opportunity to restore parity before the break. Nathan Cameron fouled Billy Sharp within striking range of goal but Coppinger, making his 250th appearance for the club, blazed his free-kick over the crossbar on 40 minutes.
Aron Gunnarsson provided an early scare in the second half, hitting a dipping drive towards the Doncaster goal which just grazed the crossbar.
On 53 minutes, McSheffrey teed up a pinpoint cross for an onrushing Jutkiewicz. The former Everton striker saw his powerful strike clatter against the crossbar and bounce clear of danger.
The under-siege hosts then received a hammer blow to their chances of recovery, losing top scorer Billy Sharp to injury on the hour mark.
Coventry had their goalkeeper to thank again with 68 minutes played, Hayter controlling a loose ball and directing a swerving strike which Quirke did well to catch. Coppinger then saw his 79th minute effort rebound off the teenager's feet.
But Hayter spoiled the visitors' evening with his ninth goal of the season, manoeuvring inside the box to find a gap and finally beat Quirke.