Martyn Waghorn's seventh goal of the season was enough to see Nigel Pearson's men seal the points and register a first win in three at a snowy Keepmoat Stadium.
The on-loan Sunderland man broke clear to fire past Neil Sullivan after early Foxes domination.
Leicester could have had more goals as Simon King wasted a fine chance and Sullivan denied Waghorn in the second half.
However, Doncaster may also feel they should have got something out of the encounter as Jamie Coppinger and Billy Sharp both went close to equalising.
Doncaster's second loss in a row could end their hopes of a late play-off bid in the closing stages of the campaign, but Leicester are very much in contention.
The visitors were quick out of the traps and spent much of the opening exchanges in the Rovers half, spurning a couple of chances to take an early lead.
First Michael Morrison headed over and then Lloyd Dyer saw his effort saved by the feet of Sullivan.
But the Foxes were not to be denied for long and they went ahead in the 12th minute.
Waghorn chased a long ball from goalkeeper Chris Weale and the on-loan striker shook off the challenge of Gareth Roberts to go through on goal before finishing in style.
Despite being void of their usual fluid passing game, Doncaster responded well and began to come into the match, with Jordan Mutch dragging his shot wide and Sharp being denied a run on goal by a cynical Bruno Berner foul.
But Rovers' emergence allowed Leicester to threaten on the counter attack, with the visitors making good use of Dyer's lightning pace.
And the winger almost set up a Leicester second when he broke at speed, but King fired his shot over from the edge of the area.
The prolonged snowfall began to settle on the pitch in a lively beginning to the second half, with both penalty areas seeing action.
Sharp hooked a shot just wide of the far post for Doncaster, while Waghorn wasted a good opportunity to get a shot away at the other end.
As the game became stretched Doncaster stepped up their search for a leveller and Coppinger was denied by a good stop by Weale, while the Leicester stopper was also called into action to keep out a Roberts effort distance.
But moments later, Rovers were reliant on a fine save from Sullivan to keep their deficit to one, when he brilliantly tipped Waghorn's effort wide.
The inevitable Doncaster onslaught duly arrived in the final 10 minutes, with James Hayter blazing wide with the goal at his mercy, but a solid Leicester defence held firm.