Doncaster held out until half time, but within two minutes of the restart they found themselves two behind courtesy of a Carl Ikeme mistake. A cross from Lee Peltier seemed to be easy for the Rovers keeper to collect, but he somehow fumbled the ball into his own net.
The Foxes got their third of the game with just over ten minutes left when Ben Marshall cut inside and fired his shot into the top corner.
The rout was completed with one minute left on the clock when Paul Gallagher beat Ikeme from just inside the penalty area.
The result means that Leicester move up to ninth in the table, while Doncaster remain bottom, now seven points away from safety.