But the Foxes – who also hit the woodwork three times – had to rely on a controversial penalty award to kickstart the rout at the Walkers Stadium.
And Doncaster manager Sean O'Driscoll was left to bemoan the pivotal penalty decision.
Billy Sharp had given Rovers a sixth-minute lead with his 100th career goal and the Yorkshire side looked comfortable until referee James Linington intervened with his disputed decision.
The ball appeared to be rolling harmlessly out of play when Rovers goalkeeper Neil Sullivan slid in on substitute Lloyd Dyer, which the official ruled was an illegal lunge. Paul Gallagher slammed home the spot-kick and further goals from Richie Wellens – against his former club - Kyle Naughton, Darius Vassell and Martyn Waghorn followed.
O'Driscoll said: "I watched it on DVD at half-time and I was gobsmacked. They both went for the ball and there was a collision. Why it warranted a penalty decision, I'm not sure."
O'Driscoll conceded his side were very poor after the restart.
He added: "We didn't really turn up in the second half. The wheels came off. Our organisation and discipline went and we paid the price."
His counterpart Sven Goran Eriksson purred: "In the second half we were brilliant, absolutely fantastic, creating chances on many occasions and playing good football."
The Swede conceded the Foxes were fortunate to be awarded their penalty. He said: "I haven't seen a replay of the penalty, but from the bench it looked a little harsh."
Eriksson ruled out stories in the media that he may quit the Foxes to take over the Iran national team.
Leicester City: Weale, Naughton, Davies, Miguel Vitor, Cunningham, Abe, Wellens, King, Vassell (Oakley 86), Bednar (Dyer 37), Gallagher (Waghorn 78). Unused substitutes: Logan, Fryatt, Moussa, Hobbs.
Doncaster Rovers: Sullivan, Martis, Thomas, Hird, O'Connor (Souza 75), Hayter, Stock, Oster, Coppinger (Wilson 86), Sharp, Healy (Shiels 76). Unused substitutes: Gary Woods, Brooker, Lockwood, Fairhurst.
Referee: J Linington (Hampshire).
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