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.
Di Canio's appointment sparked former Foreign Secretary David Miliband's resignation as vice-chairman of Sunderland and ignited much conjecture, with the former West Ham forward on Wednesday belatedly insisting he does not support "the ideology of fascism".
Former managers, team-mates and opponents praised Di Canio's character, but former goalkeeper Shaka Hislop, who played alongside him at Upton Park, called for a clarification of his views.
Di Canio, who was met warmly by Chelsea captain John Terry before kick-off, was given seven games to ensure Premier League survival.
He made three changes from O'Neill's last match in charge - last weekend's loss to Manchester United - with Connor Wickham, Sebastian Larsson and Kilgallon drafted in.
Chelsea's quest in the remaining weeks of the season is no less important than Sunderland's: to secure a return to the Champions League, after their defence of the trophy ended at the first hurdle and prompted Rafael Benitez's appointment.
Arsenal's win yesterday, coupled with the loss at Southampton last weekend, meant the Blues had slipped out of the top four prior to kick-off.
In a scrappy first half the hosts looked like a team playing their fourth game in nine days and struggled to test Simon Mignolet.Chelsea were awarded just a corner when the ball hit Kilgallon on the arm during an aerial challenge with Demba Ba - one of the Blues' five changes from Thursday night.
Sunderland were playing on the counter attack and Stephane Sessegnon found Adam Johnson, whose curling shot was blocked by Luiz before Craig Gardner was booked for a scissor-like late lunge on Ba. It might have been red.
The combination of the muscular Wickham and livewire Sessegnon caused trouble for Luiz and Ivanovic, while Johnson was enjoying his afternoon against Ryan Bertrand, but Sunderland could not test Petr Cech as Chelsea often scrambled to recover in defence.
Eden Hazard's tame header from Oscar's cross was easily saved by Mignolet, before Sunderland broke and claimed a 45th-minute corner when Luiz deflected Wickham's shot wide.
Johnson's set-piece was flicked on by John O'Shea and Azpilicueta could only deflect the ball into his own net.
Having been animated throughout, pacing in his technical area, Di Canio's celebration was muted.
Torres came on at half-time for Ba, whose movement was limited after Gardner's challenge, and his first act led to Chelsea's equaliser.
Buoyed by his double against Rubin Kazan, Torres scythed in off the left wing and found Oscar, who, for once, lost control of the ball as Mignolet raced to meet him.
The ball ricocheted off the goalkeeper and hit Kilgallon before spinning into the far corner.
Chelsea also benefited from good fortune for their second after 55 minutes.
Azpilicueta's long-range effort deflected out for a corner and Wickham failed to clear. Luiz struck a low shot which Ivanovic cleverly turned in with a back-heel.
The relief was palpable as the Blues fans sang in support of their rejuvenated team.
Hazard headed over from an Oscar cross before Gardner caught Luiz as another meaty tackle left a Chelsea player requiring treatment.Benitez was anxious enough to tell Terry to warm up, but Luiz continued.
Another moment of worry for Chelsea came when Johnson went by Mikel and curled a shot around the post.
Di Canio urged his men on and introduced James McClean for the ineffective Larsson, while Wickham was left dazed after he was caught by a Luiz elbow and required treatment.
Di Canio's former West Ham team-mate Frank Lampard was introduced for the final skirmishes but Sunderland could not find an equaliser.