Fernando Torres scored his second double of the week as Chelsea's search for an English Premier League win under Rafa Benitez ended at Sunderland on Saturday
Also, Mikel Arteta's pair of penalties secured Arsenal's victory over highflying West Bromwich Albion.
Chelsea's 3-1 win at Sunderland halted a seven-game winless run in the league — three under Benitez.
Torres, who scored twice in midweek as the holders exited the Champions League, scored his first domestic goals in two months at Sunderland and then set up Juan Mata after the break.
"We are watching now a Fernando with more confidence and with more belief, and at the same time, the team is the same way," Benitez said. "I was analyzing his movement before and we were adjusting little things. It's a question of confidence and just little different movement."
Chelsea remains third but went seven points behind leader Manchester United, which is at second-place Manchester City on Sunday.
Arsenal rose from 10th to sixth after Arteta scored twice from the spot in a 2-0 victory over fifth-place West Brom.
Queens Park Rangers remains stuck at the bottom without a win after being held to a 2-2 draw at Wigan. But Southampton climbed out of the relegation zone by beating Reading 1-0.
Reading was joined by Sunderland in the drop zone after the northeast side helped Chelsea to bounce back from its European setback.
Unlike Torres' goals against FC Nordsjaelland, which couldn't help Chelsea progress in the Champions League, his double on Saturday were crucial.
The Spain striker volleyed the ball into the net with the studs of his boot in the 11th minute at Sunderland.
And he converted his first penalty kick in English football on the stroke of halftime after Seb Larsson had fouled Ramires as the ball was just about to go out for a goal kick.
Torres had seven goals in 21 matches in all competitions this season under Roberto Di Matteo, but has now scored four in five games under Benitez, his former manager at Liverpool who replaced the Italian last month.
"If the team plays well and creates chances, Fernando will score goals," Benitez said.
Chelsea now heads to the Club World Cup in Japan for the next week.
"It's always important to win, but especially if you are going to a tournament like this," Benitez said.
At Emirates Stadium, Arsenal halted a three-game run without a win after fortuitously being awarded the first penalty, which Arteta converted in the 26th.
Santi Cazorla went down lightly under Steven Reid's challenge when his shin only appeared to be clipped slightly.
West Brom manager Steve Clarke said there was "zero contact."
"I'm not sure what the referee saw but it was a bad decision for us," he said. "It changed the shape of the afternoon."
Arsenal manager Arsene Wenger said his player told him there was contact.
"I'm sorry if it wasn't a penalty, but I have spoken to Santi and he said he had been touched and lost his balance," Wenger said.
No one disputed Arteta's second penalty in the 64th after Alex Oxlade-Chamberlain was brought down by Chris Brunt.
"I'm proud of the victory today because it's important for our season when our backs are to the wall, because our spirit has been questioned because of the flat performance last week," Wenger said.
Swansea, Arsenal's conquerors last weekend, lost for the first time in six weeks on Saturday as Norwich won 4-3 in south Wales.
Now unbeaten in nine matches, Norwich raced to a 3-0 lead by halftime after goals from Steven Whittaker, Sebastien Bassong and Grant Holt.
Swansea staged a comeback with goals from Michu and Jonathan De Guzman, but Robert Snodgrass' free kick for Norwich ensured Michu's late second couldn't rescue a point for the hosts.
At Wigan, QPR briefly looked to be on course for its first win of the season when Djibril Cisse put the visitors in front in the 71st after teammate Ryan Nelsen had cancelled out James McCarthy's opener.
But McCarthy was on target again in the 74th to clinch a draw, keeping QPR bottom and leaving Wigan just a place and two points clear of danger.
Southampton moved past Wigan on goal difference after Jason Puncheon's second-half goal secured victory over Reading.
Aston Villa is between between Wigan and Southampton after being held to a 0-0 draw at home by Stoke.
The visitors had defender Ryan Shotton sent off in stoppage time for a second bookable offence, but replays appeared to show he made no contact on Villa substitute Fabian Delph.