The Robins won away last week but have now lost their last three home games and contributed to their own downfall in this contest.
The win will do plenty for Doncaster's confidence and new manager Sean O'Driscoll, who was experiencing his first win as Rovers boss, can be pleased with the way his team defended for most of the game while taking the chances that came their way.
The visitors took the initiative from the early stages and enjoyed easily the best of the opening half.
Striker Lewis Guy turned sharply and shot across the face of goal with only two minutes played before Jonathan Forte saw an effort deflected wide off Gavin Caines after Sean McDaid had picked him out with a fine left-foot cross.
Steve Guinan volleyed high over the bar for Cheltenham but that was from a rare forage forward by the home side during the first 45 minutes.
The tide resumed in the direction of the home goal with Bruce Dyer forcing a good save from goalkeeper Scott Brown and Rovers finally making their dominance count one minute into first-half stoppage time.
Forte got away on the left and adjusted to his right foot before crossing for Guy to touch in at close range.
Cheltenham had the better of the second half but created little in front of goal until the very late stages.
By then Doncaster had doubled their advantage when a long ball forward from substitute Jason Price caused all manner of problems in the Cheltenham defence. Goalkeeper Brown and defender Shane Duff left the ball for each other and Forte nipped between them to score.
Earlier, Brown had somehow deflected a shot from Paul Green over the bar and dived to hold a shot from Dyer so the second goal was really no surprise.
Cheltenham threw defender Gavin Caines up front for the closing stages and he wasted his team's best chances, heading over from close range and volleying wide when well-placed.
By then, however, Doncaster were virtually assured of three valuable points.