Mark Hughes made one change to the side that defeated Charlton at the weekend, David Bentley returning to the starting line-up in place of the injured Ryan Nelsen.
Chelsea made eight changes to the side that wrapped up the title against Manchester United. Frank Lampard, Ricardo Carvalho and William Gallas, two of their three goalscorers, the only survivors.
The home side formed a guard of honour as Jose Mourinho's men took to the field, but that was as much respect as they were paid throughout the entire 90 minutes.
A lacklustre first half, in which Rovers' passing was more crisp and accurate, didn't come to life until just before the half-hour.
On 27 minutes, Craig Bellamy just managed to connect with Michael Gray's left-wing cross, the ball struck the crossbar and from just two yards out, Bentley somehow headed wide on the rebound.
Just eight minutes later and it was the visitors turn to be denied by the woodwork. Geremi's ball in found the outstretched leg of Eidur Gudjohnsen, but the Iceland international's effort struck the foot of the post and was cleared to safety.
But as the half looked to be ending goalless, Rovers made the breakthrough.
Geremi was booked for blocking Morten Gamst Pedersen's cross with his arm and from the resultant free-kick, Savage curled the ball into the far corner of the net.
However, replay suggested that Reid may have got the faintest of touches to head home his second goal in as many games.
As the second half got under way, Geremi was never far from the action.
His ball into the box less than a minute after the break was almost converted by Gudjohnsen on the volley, he then failed to prevent Savage's surging run and shot just a minute later, before being lucky to stay on the pitch after upending Pedersen on the left touchline.
The Blues had three second-half appeals for a penalty, all waived away, as Rovers held out for a famous home treble over Manchester United, Arsenal and Chelsea.