Chelsea was playing its fourth game in nine days but still had enough energy to come from behind, with Branislav Ivanovic netting the winner after both sides scored an own goal.
Chelsea is now back ahead of Tottenham on goal difference after its London rival drew 2-2 with Everton and dropped to fourth.
A superior goal difference is also keeping Sunderland out of the relegation zone ahead of Wigan, which drew 1-1 at Queens Park Rangers.
QPR led through Loic Remy's 85th-minute goal but Shaun Maloney equalized with a free kick in stoppage time to leave the London club a point above bottom-place Reading but still seven adrift of Wigan and Sunderland.
With the season entering its final weeks, Manchester United can effectively wrap up the title on Monday with a victory in the Manchester derby that would put the leaders 18 points ahead of Manchester City.
But the footballing action has been overshadowed in the last week by the reaction to Di Canio being handed his first Premier League management job.
Immediately after replacing the fired Martin O'Neill last Sunday, Sunderland vice chairman David Miliband — a former British foreign secretary — quit in protest at Di Canio's "past politics statements."
Further condemnation followed as Di Canio's past fascist sympathies were publicly questioned, but he took until Wednesday to formally say he does not "support the ideology of fascism."
When asked after Sunday's match about the criticism, Di Canio responded: "If I have to answer every comment it's difficult. As a person you don't change, but you become an adult, you become a manager."
The Sunderland job is Di Canio's second in management after a stint at third-tier English club Swindon.
The task handed to him by Sunderland owner Ellis Short is to keep Sunderland in the topflight. The mission got off to a good start on the stroke of halftime when Chelsea defender Cesar Azpilicueta hooked the ball into his own net after John O'Shea flicked on Adam Johnson's corner.
But Sunderland collapsed inside 10 minutes of the second half.
Two minutes after the break, substitute Fernando Torres charged down the left flank and squared to Oscar, whose shot was blocked by Simon Mignolet and the ball spun off Matthew Kilgallon's leg and drifted over the line.
Chelsea's second was also slightly fortunate, with Ivanovic appearing to be unaware the ball was heading to him from David Luiz when he turned the ball into the net.
Chelsea's sixth straight win in all competitions ensured Benitez continues to escape the abuse he faced after replacing Roberto Di Matteo in November.
"The feeling is that everybody has realized we have to stick together — we have to support the team," Benitez said. "That is the best way."
It was helped by Tottenham, without the injured Gareth Bale, throwing away the lead against Everton.
Emmanuel Adebayor put Tottenham ahead inside the first minute at White Hart Lane, turning Jan Vertonghen's cross into the net.
Phil Jagielka headed Everton level in the 15th and Kevin Mirallas skipped through the Tottenham defence before putting the visitors in front at the start of the second half.
But Gylfi Sigurdsson rescued a point for Tottenham in the 87th, reacting quickest after Adebayor hit the post.
While Tottenham is two points ahead of fifth-place Arsenal having played an extra game, Everton is a further four points adrift in sixth.
Liverpool is three points behind its Merseyside rival after drawing 0-0 with West Ham, which is six points clear of danger.
QPR's survival bid looked to have been boosted when Remy scored a sublime goal despite Harry Redknapp's side down to 10 men since Bobby Zamora was sent off in the 21st for a clumsy high challenge on Jordi Gomez.
But Maloney levelled in the fourth minute of stoppage time, sending his free kick over the wall and past Julio Cesar.
Newcastle also scored in the final moments to move five points clear of Wigan and Sunderland with a 1-0 victory over Fulham.
Papiss Cisse slotted home a pass from Yohan Cabaye in the third minute of added time.