City have made remarkable progress since Robins took charge three months ago and he said: "I'm made up for the players and the fans - this was our best performance since I came to the club".
Franck Moussa volleyed home in the third minute and Rovers squandered chances before David McGoldrick added the second.
On-loan Nottingham Forest striker McGoldrick missed a good chance to score again before he added the third from close range in the 58th minute.
Rovers tried hard to fight back and Chris Brown pulled one back with a header in the 76th minute before Adam Barton wrapped up the points for Coventry in fine style with a superb strike in the last minute.
Robins added " We got all aspects of our game right and the competitive side was particularly pleasing because we won most of the second balls and dealt with the aerial bombardment brilliantly.
"It would have been nice to have kept a clean sheet but if you can score four goals I'm not going to complain about that."
Doncaster boss Dean Saunders felt two-goal McGoldrick was the difference between the sides.
Saunders said " It was a disastrous result for us . Conceding four goals is totally unlike us and I can only put it down to a bad day at the office. We didn't defend well at all and that's really been our strength this season.
"You have to give Coventry credit and especially McGoldrick for the way he took his goals."