Second half goals from Branislav Ivanovic and Nicolas Anelka condemned Rovers to defeat at the hands of Chelsea.
In a game in which the home side had the better of play throughout, Rovers were helped by the woodwork in the first half as first Ramires and then Anelka were thwarted by the crossbar.
The lively Junior Hoilett had Rovers' best effort, but Petr Cech was equal to his efforts, diving to his right to save.
The second half was one way traffic with the opening goal coming on 57 minutes. Ivanovic turning and firing through a crowded area from Florent Malouda's corner.
Chelsea's second also came from a set piece, again a Malouda corner found Ivanovic, the Serbian's header needing a final touch from Anelka to find the back of the net.
Roque Santa Cruz played the second half on his Rovers return, but it was an afternoon in which the Rovers frontmen saw little of the ball.
Ahead of the game Rovers made five changes from the side that defeated Queens Park Rangers in last week's FA Cup win.
Steve Kean was able to welcome back Paul Robinson, Christopher Samba, Martin Olsson, David Dunn and Niko Kalinic with Mark Bunn, Grant Hanley, Jason Lowe, El-Hadji Diouf and Benjani all dropping to the bench along with Friday signing Roque Santa Cruz.
Rovers started with Junior Hoilett behind Kalinic up front, with Mame Biram Diouf on the right, but it was from his side that Chelsea threatened early on.
A 2nd minute Florent Malouda corner found its way through to the edge of the area and whilst Hoilett was caught in two minds about clearing the ball Ramires stole in to crash his effort off the crossbar. An early escape.
Rovers fashioned an early chance of their own two minutes later, Martin Olsson stinging the gloves of Petr Cech after the visitors broke quickly through Kalinic.
But it was largely one way traffic with the home side pressing, earning a series of corner kicks in the process, but Rovers, superbly marshalled by the likes of Ryan Nelsen and Gael Givet, held firm.
Then as Didier Drogba somehow avoided a clear offside, Givet did brilliantly to race back and tackle the Ivorean in the area.
One challenge two many with Frank Lampard saw David Dunn replaced at the midway point at the half, his replacement Jason Lowe coming on for his Premier League debut.
And after Junior Hoilett had seen his effort from the edge of the area saved by Cech, Jason Lowe pounced on the rebound but Chelsea captain John Terry was alert to make an important block.
As the first half drew to a close Chelsea ended on the up, Nicolas Anelka unfortunate to see his swept effort bounce off the corner of post and bar from Drogba's centre.
Roque Santa Cruz didn't have long to wait to make his return in a Rovers shirt as he emerged on the pitch at the start of the second half. The Paraguayan replacing Niko Kalinic but, like the Croatian before, Santa Cruz would have a quiet afternoon up front as the home side would dominate the second period.
Nicolas Anelka signalled Chelsea's intent when he fired a yard wide of goal sixty seconds after the restart, and aside from a Mame Biram Diouf header from a Pedersen corner that went wide, it was the home side who had all the pressure.
That buit progressively until the deadlock was finally broken just before the hour mark when from a Malouda corner kick, Pedersen couldn't get enough on his headed clearance and the ball fell to Branislav Ivanovic who poked home past an unsighted Paul Robinson from close range.
Rovers brought on Jason Roberts in response to going behind, but John Terry very nearly doubled the home side's lead when he nodded a Frank Lampard effort wide of goal.
However Steve Kean's side were the makers of their own downfall. Chris Samba's woefully underhit backpass saw Drogba in, and although Robinson saved brilliantly, he was powerless from the resulting corner kick as Anelka poked home Ivanovic's downward header.
Malouda brought about another save from Robinson, before Didier Drogba was just wide as the home side closed out the game comfortably.
CHELSEA: Cech, Ivanovic, Cole, Essien (sub McEachran 80 mins), Ramires, Lampard, Drogba, Malouda (sub Sturridge 87 mins), Bosingwa, Terry (c), Anelka (sub Kalou 80 mins).
Subs not used: Turnbull, Mikel, Ferreira, Bruma.
ROVERS: Robinson, Salgado, Samba (c), Nelsen, Givet, MB Diouf, Dunn (sub Lowe 24 mins), Pedersen, Olsson, Hoilett (sub Roberts 68 mins), Kalinic (sub Santa Cruz 46 mins).
Subs not used: Bunn, EH Diouf, Benjani, Hanley.
Booked: Malouda (Chelsea)