The build up to Di Canio's first match as successor to Martin O'Neill was overshadowed by debate over the controversial Italian's character after his 2005 statement proclaiming to be a "fascist but not a racist" and he could not prevent Sunderland's winless run extending to nine games.
Chelsea trailed at half-time to Cesar Azpilicueta's own goal, but Matt Kilgallon deflected into his own net following a surging run by substitute Fernando Torres and Branislav Ivanovic directed a David Luiz shot into the Sunderland goal to put the Blues in front after 55 minutes.
It proved to be the winner as Chelsea, who beat Manchester United on Monday and Rubin Kazan on Thursday, returned above Tottenham on goal difference and into third place.
The Blues' attention now turns to Thursday's trip to Moscow for their Europa League quarter-final second leg with Rubin before next weekend's FA Cup semi-final with Manchester City at Wembley, while next for Sunderland is a Tyne-Wear derby at Newcastle.
Earlier, Gylfi Sigurdsson's late strike prevented Tottenham from slipping to another defeat, but Spurs' reliance on Gareth Bale was laid bare as they had to settle for a 2-2 draw against Everton at White Hart Lane.
The Toffees looked like taking all three points from north London after Phil Jagielka and Kevin Mirallas scored following Emmanuel Adebayor's 35th second opener.
But Sigurdsson, charged with the task of playing in the hole where Bale has been so effective this season, salvaged a point for the hosts by scoring a crucial goal three minutes from time.
Despite finding the net twice, Tottenham sorely missed the scoring talents of Bale and the creative wizardry of Aaron Lennon.
And Sigurdsson's last-gasp equaliser will not mask Tottenham's precarious predicament. For if Arsenal beat Everton in their game in hand, they will leapfrog their bitter rivals in the hunt for Champions League qualification.
And with games against Chelsea and Manchester City to come in their final six games, there is an inescapable feeling that Tottenham are in the process of throwing away their Champions League dreams once more.
Loic Remy appeared to have given Rangers renewed hope in their survival quest with a stunning 85th-minute strike, only for Maloney to drive home a ferocious equaliser from 20 yards just seconds from the final whistle.
It was a spectacular twist to the match and agonising for QPR who had played all but 20 minutes with only 10 men after Bobby Zamora was sent off for a moment of madness.
In attempting to reach a throw in, Zamora kicked Jordi Gomez, striking the Spanish midfielder in the head with his studs and dropping him to the floor.
Gomez received treatment and having consulted assistant Scott Ledger, referee Phil Dowd sent Zamora off.
It was an inexplicable act from the England forward given his side were in control at the time and the 32-year-old will now miss crucial fixtures against Everton, Stoke and Reading - with his side seven points from safety.
Alan Pardew's side - and Cisse especially - had previously spurned a catalogue of chances at St James' Park against a Cottagers side who suffered their first defeat in six games.
But with frustration and anxiety growing, the Senegal forward finally beat Mark Schwarzer in the third minute of added-on time for his 11th goal of the season.
After a run of three straight defeats - two in the Premier League and a 3-1 loss to Benfica on Thursday in the first leg of a Europa League quarter-final tie - this was a crucial win for the Toon.
Three weeks after that dismal defeat at Southampton, Brendan Rodgers' side once again failed to spark, skipper Steven Gerrard coming closest to a winner when his effort was cleared off the line by the outstanding James Tomkins.
But the Hammers, for whom James Collins was equally impressive, also had a claim on the spoils, with Lucas Leiva denying them a first Anfield win in 50 years when he turned away Jack Collison's header five minutes from time.
A rather complicated scenario for European qualification is unfolding, in which finishing sixth in the might be enough.
It is not one Liverpool can afford to rely on though, which means an all-out assault on the top five.