A youthful Rovers side ended the 2011-12 campaign with a 2-1 defeat at Stamford Bridge.
Debutant goalkeeper Jake Kean was the star of the first half after the 21-year-old made a string of fine saves but he was powerless to prevent goals from John Terry and Raul Meireles giving the home side a 2-0 half time lead.
Rovers regrouped in the second half, taking the game to Chelsea, and they got their reward on the hour mark when following Morten Gamst Pedersen's corner, Scott Dann headed goalless and Yakubu nodded home.
Ramires struck the crossbar with a audacious effort, whilst Junior Hoilett and Martin Olsson went close for Rovers but they couldn't get a leveller to reward their efforts.
For the final game of the season Steve Kean made four changes from the side that tasted defeat at home to Wigan Athletic.
With injuries biting, Rovers were without Paul Robinson, David Dunn and Bradley Orr for the Chelsea fixture, meaning a debut for Jake Kean in goal and returns for Adam Henley, Marcus Olsson and Mauro Formica.
There may have been little to play for for either team but the first half was a whirlwind, particularly for debutant Jake Kean.
The 21-year-old was kept busy throughout, starting in the 2nd minute when he pushed aside a dangerous centre from Ryan Bertrand.
Rovers responded with their best chance of the half, Jason Lowe letting fly with a thunderous effort, it deflected off Raul Meireles on its way to goal with Ross Turnbull having to be alert to tip the ball over the bar.
Aside from that chance it was all Chelsea, Adam Henley making a vital challenge to steal the ball off Daniel Sturridge. Moments later Jake Kean saved well at the feet of Romelu Lukaku, then the young Rover made a one-handed save after a Sturridge cross deflected off Givet.
Chelsea continued to press, Sturridge should have done better when he headed wide at the back post, before Meireles saw a snapshot claimed by Kean.
Just past the half hour Rovers' resolve was finally broken, as Lukaku ploughed down the right he cut back to deliver a left-footed cross which was met perfectly by John Terry as he headed back across goal and into the net.
Four minutes later and the lead was doubled, and again Kean had no chance. Chelsea thought they were about to be awarded a penalty after Givet had tripped Michael Essien in the box. Just as Referee Lee Mason blows for the foul Raul Meireles toe pokes the ball into the corner of the net with the referee allowing the goal to stand.
Rovers made a change at the break with Josh Morris coming on for Mauro Formica, and the flighty wide man fashioned the first Rovers chance of the second half.
Cutting in from the left, the 20-year-old exchanged passes with Yakubu to let fly from the edge of the area, but on his weaker right foot the shot lacked purchase and was easily claimed.
On 60 minutes Rovers reduced the deficit with a well-taken goal from a corner. Morten Gamst Pedersen swinging the ball over from the left to the back post where Scott Dann headed goalwards and Yakubu applied the finishing touch for his 18th goal of the season.
Chelsea went straight up the other end and were a whisker away from making it three. As Jake Kean came to claim a ball Scott Dann headed away leaving the goalkeeper stranded, Ramires nonchalantly flicked the ball goalwards only for it to bounce off the top of the bar.
Junior Hoilett lashed an effort narrowly over after a bursting run whilst at the other end Kean was called into action once more with a fingertip save after Daniel Sturridge's shot deflected off Martin Olsson.
Ruben Rochina and David Goodwillie were brought on as Rovers went looking for an equaliser, but it was the home side who spurned the best chance when Sturridge headed wide when it seemed easier to score.