Morrison's 85th-minute penalty gave the Sky Blues a deserved victory, in a match in which they hit the woodwork four times and missed a spot-kick.
Doncaster, who went into the game having won four matches on the bounce, had the best of the first-half possession but Coventry struck the frame on three occasions.
The first chance came in the 13th minute when Patrick van Aanholt's cross was headed towards goal by Freddy Eastwood only for the ball to bounce off the post and clear.
City's second chance could have caused a massive controversy. Referee Rob Shoesmith stopped play for a head injury by the halfway line and restarted with a drop ball. Leon Best hoofed the ball towards Neil Sullivan's goal, but it lobbed the former Wimbledon keeper and smashed off the bar.
Best and Sullivan were involved in the game's next major incident, when the keeper brought down the striker for a 43rd-minute penalty. Best stepped up to take the kick, but saw his blasted effort rebound off the post to safety.
The Best and Sullivan battle continued in a frantic second period. Best chested down a Michael McIndoe cross in the 52nd minute and fired off a volley, but Sullivan pushed it wide for a corner.
Doncaster should have taken the lead minutes later when a surging John Oster run and cross in the City box eventually saw the ball fall to the unmarked Dean Shiels eight yards from goal, but he spooned the opportunity.
Coventry dominated play and hit the woodwork for a fourth time in the 73rd minute when Aron Gunnarsson looped a ball towards McIndoe and his volley hit the bottom of the post and out for a goal kick.
Chris Coleman decided to gamble by switching Best and Eastwood for Morrison and Gary Madine and, five minutes after their introductions, the gamble paid off.
Madine went to win the ball in the air but was pushed by James Chambers - and referee Shoesmith awarded another penalty.
Morrison stepped up and fired a low shot into the bottom corner of the net for his seventh goal of the season.