Roberto Di Matteo's side claimed back-to-back wins despite a stirring late Aston Villa comeback, thanks to a double from Ivanovic and goals from Sturridge and the Spanish striker.
A dramatic second-half comeback was doused by two late Chelsea goals as Ivanovic headed home and Torres slid his shot below Shay Given.
The Blues have made it six wins in eight games under Roberto Di Matteo.
Aston Villa's inexperienced lineup was guilty of some sloppy defending that was punished clinically by Sturridge in the first half and Ivanovic twice in the second period, while Torres was a textbook counterattack in the dying seconds.
The hosts did show some fight as James Collins' firm header pulled a goal back before Eric Lichaj equalized but that merely provoked Chelsea to score two more after almost passing themselves into a stupor.
On an emotional day and with little left to play for, Alex McLeish opted to pick a youthful starting XI. Nathan Baker, Gary Gardner and Andreas Weimann all began the game, replacing Alan Hutton, Emile Heskey and Stilyan Petrov, who chose to attend the game after discovering he is battling leukaemia.
Didier Drogba was missing for Chelsea and so Torres led the line, while Ivanovic returned from injury.
Di Matteo's side started quickly and David Luiz's perfectly weighted through pass had Torres in on goal after just five minutes. But the Spaniard's hesitancy allowed Collins to apply enough pressure to help Given's smother the shot and prevent the goal.
Aston Villa's inexperience showed immediately and as Salomon Kalou crossed from the left and Torres touched the ball into Mata's path. Given advanced and the midfielder returned the pass to his fellow Spaniard.
Despite Steven Warnock's excellent block as Torres seemed set to score, Sturridge pounced to slam the ball home and crown his 50th Chelsea appearance with a goal.
Villa's untried forward line showed glimpses of promise as Weimann dropped deep to combine well with his captain Gabby Agbonlahor but both struggled to create a clear goalscoring opportunity in the opening stages.
At the other end, John Obi Mikel's deflected drive from 25 yards was well dealt with by Given.
On the 19th minute, Villa Park rose to support the club captain Petrov, delivering a minute's applause and it almost culminated in an equalizser as Collins nodded a corner just over the bar.
There followed a period of jousting in which neither side created a glaring opportunity. The best efforts came as Baker volleyed over from a corner and Sturridge hit an ambitious 25-yard shot at Given.
As halftime approached, Villa carved its best chance as Barry Bannan controlled Weimann's cross on the right side of the area. His layoff to Agbonlahor gave the striker the space to touch and strike low at goal but Petr Cech saved fantastically with his legs after initially misreading the direction of the effort.
Seconds before the interval, Gary Cahill replaced Luiz who appeared to have picked up a minor knock.
Neither side made any halftime changes but the effect of McLeish's team talk propelled Villa into a promising start to the second period.
Despite an encouraging spell of possession, Chelsea doubled its lead with its first meaningful attack just five minutes after the break.
Mata's corner evaded Frank Lampard at the near post and landed invitingly at Ivanovic's feet. The Serbian defender accepted the gift, smashing a snapshot past Given for his first league goal of the season.
Then, the game died. Any fight left in Villa was extinguished and Chelsea controlled proceedings at a canter. In truth, Villa could have scored more had it had the desire to do so.
As it stood, the best chance up until the 75th minute was a Torres header from Ivanovic's curled cross, but that drifted harmlessly wide.
Florent Malouda came on for Mata and went up front – an indication of how lightly the visitors were taking the final stages.
But there was a twist as Collins met a long throw to plant his header past Cech and give Villa a goal. Suddenly, the fans in the Holte End awoke and there was a game on once again.
Villa buoyed by a rare goal, pressed Chelsea as it sought an unlikely equalizer. Mark Albrighton collected the ball on the left flank before attacking Ivanovic.
His low cross traveled between Cech and his defenders and as Ashley Cole showed trepidation at the back post, Lichaj arrived to poke home Villa's second. Chelsea had thrown it away.
Or had it? Di Matteo's side showed the response expected from Champions League quarterfinalists and Ivanovic headed home his second of the game from another corner.
Torres provided the assist with a deft front post flick and it looked like Chelsea had got out of jail with five minutes to play.
Villa pressed for another late surprise but, this time, the Chelsea defense held firm, led by captain John Terry. Sturridge led a last minute counterattack and he assisted Torres for a rare goal as he controlled the pass and smashed the ball low past Given.