The Blues, who had recorded just one win from their previous nine Premier League games, made a blistering start and it needed a fine challenge from Michel Salgado to prevent Didier Drogba from opening the scoring.
Ramires rifled a half-volley against the crossbar before Drogba hesitated to allow Gael Givet to make a last-ditch, and they were almost punished at the other end but Petr Cech saved well from David Hoilett.
Back on the attack, Nicolas Anelka curled a shot wide and Frank Lampard failed to get a head on target as Chelsea continued to waste chances, and the former then struck the corner of the post and crossbar as the first half ended goalless.
Anelka, who has a prolific record against Rovers, again went close after the interval, but the opener did finally arrive on 57 minutes when John Terry flicked on a corner and Branislav Ivanovic rifled the ball home.
Terry headed agonisingly wide as Chelsea sought a second, which Christopher Samba almost gifted to them when his dreadful backpass let in Drogba only for Paul Robinson to spare his defender’s blushes.
However, from the resulting corner the champions wrapped up the points when Ivanovic rose highest to head the ball into the path of Anelka, and the Frenchman directed it past Robinson.