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The Foxes were indebted to referee James Linington though, as he awarded the hosts a controversial penalty just before half-time when Lloyd Dyer was adjudged to have been brought down by Rovers goalkeeper Neil Sullivan.
There appeared to be minimal, if any, contact between the two players but Paul Gallacher powered his spot-kick past the unfortunate keeper to cancel out Billy Sharp's acrobatic effort.
Leicester took full advantage of that slice of luck in the second half with four unanswered goals.
First, Richie Wellens' superb 35-yard strike flew past Sullivan and the midfielder turned provider as he teed up Kyle Naughton, who made no mistake when through on goal.
Darius Vassell made sure of the points with his first goal for Leicester as he slid the ball under Sullivan and Martyn Waghorn deepened Doncaster's woes as he tapped in from close range in added time.
It was Sean O'Driscoll's men who started brightly though and Sharp - on his return to the starting line-up - put them in front after six minutes.
James Coppinger dribbled the ball to the right by-line before his chip into the box found Sharp and he brought up the 100th goal of his career in fine style by hammering his volley home.
It was no more than the visitors deserved as just moments earlier, James Hayter had scuffed a shot wide when clean through on goal.
As the half wore on, Leicester started to get themselves back into the match and nearly equalised when Andy King headed against the bar from Greg Cunningham's corner.
However, they should have found themselves two down as Curtis Davies' back pass was intercepted by David Healy and after the on-loan striker rounded Chris Weale, he somehow sliced the ball wide of the net.
It was a terrible miss for the Northern Irishman, who has recently extended his loan from Sunderland by another month.
He was made to rue the miss as the hosts equalised on the stroke of half-time in controversial circumstances.
Substitute Dyer, who replaced the injured Roman Bednar in the 37th minute, latched on to Wellens' back heel before he was adjudged to have been brought down by Rovers goalkeeper Sullivan.
Gallagher duly fired past Sullivan and buoyed by that stroke of luck, the hosts started the second half well.
Davies headed wide from Gallagher's left-wing corner and Cunningham rattled the bar with a fiercely struck 20 yard free-kick.
Their pressure eventually told though and Wellens put Leicester in front with a brilliant solo goal against his former club in the 61st minute.
The midfielder collected the ball on the halfway line and brought it forward before drilling an unstoppable long-range thunderbolt past Sullivan.
Wellens was at the centre of things when Leicester extended their lead as his perfectly weighted pass found Naughton and the defender held his nerve to slot home.
Vassell ensured victory 15 minutes from time when he latched on to Dyer's through ball and slid the ball under Sullivan.
Waghorn wrapped up the win in injury time when he tapped in after King's angled shot had struck a post.