Ledesma made the most of some poor defending midway through the first half to double his side's lead after Dexter Blackstock had grabbed an early opener.
With Doncaster showing some strong early season form and Rangers heavily tipped to achieve promotion, this clash promised to be an intriguing one.
But from the moment Blackstock put the home side in front on five minutes, the visitors were always chasing the game and ultimately never recovered.
Daniel Parejo's free-kick caused confusion at the far post and Blackstock was the man to profit, bundling home from four yards out to open his Championship goal account for the season.
Rovers immediately went in search of an equaliser, leaving themselves exposed at the back with Rangers playmakers Parejo and Ledesma orchestrating several dangerous counter-attacks.
Parejo should have doubled the lead on 26 minutes but blazed his header over from Peter Ramage's cross as Doncaster's defence continued to wilt.
And they were punished two minutes later when Mikele Leigertwood launched a long ball forward and the Doncaster centre-backs allowed Ledesma time and space to poke the ball past keeper Neil Sullivan.
Iain Dowie's men continued to play with pace and power, while the visitors' attractive build up play lacked any real penetration.
The finally fashioned a decent chance on the hour when the impressive James Coppinger pinched the ball off Damien Delaney in the area before firing his effort into the side-netting.
But they never looked capable of breaking through Rangers' strong rearguard despite the best efforts of Gareth Taylor and Coppinger.
And the visitors' misery was compounded when record signing Matt Mills was taken to hospital with a suspected broken jaw late in the game.