The relegated Bees looked lively at the start but soon lost their way when Doncaster began to assert themselves.
It was a typical end-of-season affair for most of the first half with goalmouth chances few and far between.
But the home side began to raise their game before the interval with Brian Stock heading inches wide before Lewis Guy failed to capitalise on a good chance when he fired straight at keeper Stuart Nelson from point-blank range.
But the breakthrough came in first-half stoppage time following a piece of quick thinking by Stock.
He noticed Nelson standing too far to one side of his goal as he lined up to take a free-kick and blasted the ball in the other direction. Nelson dived full length to tip the shot away but Adam Lockwood followed up to blast the ball home.
Osborne's dismissal in the 61st minute for kicking out at an opponent did not help the Brentford cause.
They went 2-0 behind five minutes later when James Coppinger sent Mark Wilson charging through the middle and the former Manchester United and Middlesbrough midfielder scored with a low left-foot shot in fine style.
Jonathan Forte hit the crossbar with an angled drive soon after. Little had been seen of the Brentford attack in the first half apart from a good effort from Charlie Ide that was tipped round the post by Neil Sullivan.
Guy sealed victory from the penalty spot after Adam Griffiths had brought down Forte 15 minutes from time.
It was Doncaster's first home win in four games and Brentford's 11th consecutive match without a victory.