The Blues finally stopped the rot as arguably their best league performance for more than two months saw them beat Rovers and climb back into the top four.
Looking to end their worst run in the league for almost 15 years after winning just one of their previous nine games, Chelsea dominated from start to finish at the Bridge.
Both their goals came from corner kicks courtesy of Ivanovic and Anelka, with their final ball continuing to let them down in open play.
The duo also found the net against Rovers back in October to keep Chelsea five points clear at the top of the table, but their efforts on Saturday were arguably even more precious.
Despite reports he might attend the game, there was no sign of billionaire owner Roman Abramovich prior to kick-off.
Chelsea needed no extra motivation to end their miserable run in the league, knowing they could leapfrog fourth-placed Tottenham for at least 24 hours.
And buoyed from Sunday's 7-0 FA Cup thrashing of Ipswich and having recalled all their big guns, the home side flew out of the traps.
A heavy touch from Didier Drogba allowed Michel Salgado to intercept after the striker was played in by Anelka and Ramires smashed the ball against the bar after David Hoilett was caught napping.
Martin Olsson tested Petr Cech from 25 yards at the other end as the hesitancy that has dogged the champions in recent weeks began to resurface.
Michael Essien sent a difficult header wide from Frank Lampard's corner, with Blackburn's defence continuing to hold firm in the opening quarter.
Drogba fired over from range before the visitors suffered a 24th-minute blow when David Dunn limped off to be replaced by Premier League debutant Jason Lowe.
Jose Bosingwa blazed over from 25 yards as Chelsea began to run out of ideas but a lightning break 12 minutes from half-time might have seen them break the deadlock but for a brilliant Gael Givet challenge on Drogba.
They were almost caught out themselves moments later when they gave Hoilett space to shoot and force a fine save from Cech, with only desperate defending preventing Nikola Kalinic and Lowe pouncing on the rebound.
An under-pressure Lampard nodded over Bosingwa's cross from point-blank range before Anelka was desperately unlucky not to score when he flicked Drogba's wicked ball against the
Roque Santa Cruz came on at half-time for his second Blackburn debut, with Kalinic withdrawn, but the new man was almost upstaged by Anelka, who dragged narrowly wide less than two minutes in.
Florent Malouda talked himself into a booking after a poor tackle on Mame Biram Diouf, who was too off balance to head Morten Gamst Pedersen's corner on target minutes later.
Chelsea finally got the goal their overall dominance deserved in the 57th minute.
Pedersen flicked John Terry's header from Malouda's corner straight to Ivanovic, who held off Ryan Nelson before squeezing a shot past both him and Salgado.
Malouda fired straight at Robinson as the champions looked for a quickfire second, which Terry should have provided when he flicked Lampard's mishit volley just wide midway through the half.
A well-placed Lampard then got the ball stuck beneath his feet, chipping straight into Robinson's arms before Hoilett was replaced by Jason Roberts.
Robinson came to his side's rescue again 15 minutes from time when a horrendous backpass from Christopher Samba sent Drogba clear.
The striker should have scored but the keeper still did well to close him down.
But that good work was undone by more poor defending from the subsequent corner, Ivanovic leaping highest to head goalward, with Anelka making sure from point-blank range.
That was the striker's final contribution as he and Essien made way for Salomon Kalou and Josh McEachran for the final 10 minutes.
Lampard's lame finish wasted a great chance to make it 3-0, Malouda's rocket was almost spilt into his own net by Robinson and Drogba clipped a improvised strike just over the top.
Daniel Sturridge replaced Malouda for the final three minutes and Chelsea comfortably played out time.