Lee Peltier, Ben Marshall and substitute Paul Gallagher all scored in the second half, adding to the goal from Danny Drinkwater that gave the Foxes the half-time lead at the Walkers Stadium on Saturday.
The three points saw Nigel Pearson's side climb three positions to ninth in the table, five points adrift of sixth-placed Cardiff with five matches remaining.
A fifth defeat in six league games leaves Doncaster bottom of the standings and seven points from safety.
There were chances at both ends early on.
Carl Ikeme helped a long-range effort from David Nugent over the crossbar before Rovers responded through James Coppinger and Giles Barnes, but neither managed to work Kasper Schmeichel in the home goal.
Nugent threatened again before Doncaster's plans were upset by an injury to Frederic Piquionne after 20 minutes. It looked like the on-loan striker suffered a calf problem and he was replaced by Chris Brown.
Richie Wellens and Drinkwater headed chances over the bar before the latter opened the scoring in superb fashion.
Wellens' ball over the top was headed into Drinkwater's path by Nugent and the former Manchester United trainee hit a left-footed shot into the bottom corner from the edge of the box.
Brown missed the target with a header before Nugent worked Ikeme at the other end just before half-time.
Soon after the restart, disaster struck for Doncaster.
Peltier beat his man down the right-hand side before sending a harmless-looking cross into the six-yard box. But the ball squirmed through Ikeme's hands and into the net.
Herita Ilunga was next to send a header over as Doncaster tried to get a goal back, but any hopes of a comeback were extinguished with 12 minutes remaining when Marshall maintained his recent good form with another goal of quality.
The winger cut inside from the left and arrowed a right-footed shot into the top corner, giving Ikeme no chance.
Nugent hit the crossbar with an effort from the edge of the box after 83 minutes before Gallagher completed the rout with two minutes left.
Gallagher, a 61st-minute replacement for Lloyd Dyer, rounded off a nice passing move involving Marshall and Andy King by finding the bottom left-hand corner from 18 yards out.
