Terry and Meireles - who are suspended for next weekend's clash with Bayern Munich - both found the net within three first-half minutes against already-relegated Blackburn.
Ayegbeni Yakubu's 18th goal of the season halved the deficit but Chelsea ended their poor league campaign on a high in what could be caretaker manager Roberto Di Matteo and striker Didier Drogba's final home game at the club.
The supporters made their feeling about the pair clear by chanting "There's only one Di Matteo" and "Didier Drogba, we want you to stay", but that may not be enough to convince billionaire owner Roman Abramovich to sign them up.
Di Matteo rested all of his likely line-up for the Champions League final, with his other two suspended players - Ramires and Branislav Ivanovic - also starting, while Romelu Lukaku and Sam Hutchinson made their full league debuts.
The Italian, who may need to win next weekend to keep his job, picked a team that emphasised the dead-rubber nature of this match, with Chelsea already guaranteed sixth position and relegated Rovers 19th.
But there were a few players in the Blues side playing for places in Saturday's squad, one of whom, Florent Malouda, caused chaos in the Blackburn box with a fine cross inside two minutes.
Goalkeeper Ross Turnbull then went a little way to redeeming his performance in Tuesday's 4-1 thrashing at Liverpool with a fine tip over from Jason Lowe's deflected drive.
A poor touch onto a ball over the top let down Daniel Sturridge, Lukaku misdirected a header from a corner and also failed to bundle his way past Blackburn debutant Jake Kean as Chelsea continued to threaten.
Kean denied Lukaku again in the 20th minute with a fine save as he slid in to convert a low cross from Sturridge, who got his header all wrong moments later from the Belgian's cross.
Half-hearted chants of "Kean out!" were directed at Blackburn boss Steve Kean throughout the opening quarter, with Chelsea in complete control.
A goal looked inevitable and it arrived in the 31st minute after Terry decided to get involved in the Blackburn half before bursting into the box to power a header from Lukaku's excellent cross into the top corner.
It was 2-0 three minutes later as Michael Essien got around the back of the Blackburn defence far too easily before squaring for Meireles to drill into the bottom corner from 18 yards.
Lukaku nearly set up a third goal six minutes from half-time when Kean saved well from Ramires, who almost danced his way through moments later.
Unlike Kean, Di Matteo was enjoying vociferous backing from his club's fans, who also applauded the arrival of Paulo Ferreira for Malouda two minutes before the break.
Blackburn withdrew Formica for Josh Morris at the restart and the new man arguably had their best chance when he side-footed tamely at Turnbull.
But Chelsea had already gone close again through a lovely turn and shot from Sturridge, while Lukaku had also dragged wide.
That was the striker's final significant contribution as Di Matteo sent on Drogba for what could be the Ivory Coast star's farewell to Stamford Bridge.
A chorus of "Didier Drogba, we want you to stay," immediately rang out at Stamford Bridge.
The home fans were silenced on the hour mark when Yakubu pulled a goal back, glancing home Scott Dann's header from a Morten Gamst Pedersen corner.
Although they were almost cheering again when Ramires lifted the ball onto the crossbar after pouncing on a loose header.
Kean tipped Sturridge's deflected half-volley wide before Fernando Torres came on for Hutchinson, and Pedersen was withdrawn for Ruben Rochina for the final 20 minutes.
David Goodwillie arrived for Yakubu after Sturridge horribly miscued a volley, the striker making amends with an excellent cross that just evaded Ryan Bertrand.
Chelsea were cruising to victory, and although Bertrand was booked in the final minute for tugging back Olsson, Sturridge should have made the game safe when he chested wide from three yards.