The England winger scored the game's only goal midway through the first half in which Rovers twice struck the woodwork.
The home side pushed hard for an equaliser all afternoon, but Chelsea ground out the victory which keeps their title challenge on course.
Before the game, both managers rang the changes following differing midweek results in the Carling Cup.
Rovers made three changes to the side that lost 3-2 at home to Arsenal, with Brett Emerton, Zurab Khizanishvili and Tugay replacing Robbie Savage, Chris Samba and Matt Derbyshire.
Meanwhile, Chelsea made four alterations to the side that knocked out Liverpool, with Paulo Ferreira, Ashley Cole, Alex and Joe Cole coming in for Wayne Bridge, Juliano Belletti, Tal Ben Haim and Scott Sinclair.
Keen to avenge a run of three straight defeats, Rovers came flying out of the traps.
Playing in his favoured free role, David Bentley almost single-handedly ran the show for the opening quarter of the game.
He made his intentions clear with a marauding run down the right inside the first minute and fired a dipping shot from the edge of the box that skimmed the roof of the Chelsea net.
In between, Roque Santa Cruz had a goal-bound shot deflected wide for a corner and from the resultant Morten Gamst Pedersen in-swinger, Ryan Nelsen just failed to get the telling touch at the near post.
Bentley was at it again on 11 minutes, curling a right-foot free-kick onto Petr Cech's bar after he had been scythed down by Alex and after some more magic from the England man in midfield saw Santa Cruz scampering towards goal, but his angled shot drifted agonisingly wide of the far post.
Against the run of play, the home side were given a warning on 21 minutes when Andriy Shevchenko blazed over after the Rovers defence failed to clear their lines from a corner.
Then just a minute later, Chelsea took the lead as Salomon Kalou played the defence-splitting pass to Joe Cole and the wily winger brilliantly blasted the ball into the top right-hand corner of Brad Friedel's goal.
The woodwork came to the rescue of both sides just past the half-hour mark as Steven Reid's right-foot shot from Santa Cruz's centre was superbly pushed onto the bar by Cech, before Frank Lampard was allowed to run unchallenged and his equally crisp effort cannoned back of the post.
Rovers had the final chance of the half as another Bentley free-kick was again glanced onto the roof of the Chelsea net by the head of Khizanishvili.
The second half took time to get going with David Dunn's goal-saving tackle on Michael Essien the only chance of note in the opening exchanges.
Cech was forced off through injury shortly after and his replacement, Hilario, almost gifted Rovers an equaliser when he flapped at Bentley's corner only for Santa Cruz to send a free header wide of the mark.
The Portuguese keeper made amends moments later, however, when he pulled off a sensational save to deny another Santa Cruz header from Dunn's delivery.
Despite defending for much of the match, Chelsea had sufficient quality in their team to test Rovers when required as Lampard's left-foot shot was palmed round the post by Friedel, before the big American got down well to deny a header from Kalou.
Six minutes of additional time were played, but the visitors held on to inflict a fourth straight defeat on the team in blue an white.