Manchester City revived their Premier League title bid after a 2-0 win away to Crystal Palace on Sunday saw them move to within three points of leaders Liverpool with a game in hand.

Edin Dzeko's fourth-minute header put City ahead before Yaya Toure doubled their lead shortly before half-time when he curled a shot beyond goalkeeper Julian Speroni.

Victory also left City just a point behind second-placed Chelsea, who beat table-toppers Liverpool 2-0 at Anfield earlier on Sunday.

Significantly, Manuel Pellegrini's City side still have three league games to play this season compared to Liverpool and Chelsea's two apiece.

If City and Liverpool win all their remaining league matches they will both finish with 86 points.

However, City currently have a superior goal difference of +58 compared to Liverpool's +50 and Chelsea's +43.

Shortly before City kicked-off at Selhurst Park, Chelsea kept their hopes of an English and European double alive with victory at Anfield.

Senegal striker Demba Ba gave Chelsea the lead in first-half stoppage time when a slip by Liverpool captain Steven Gerrard allowed him to charge through and beat Reds goalkeeper Simon Mignolet in a one-on-one.

Chelsea put the result beyond doubt in added time at the end of the match when, with the hosts pressing for an equaliser, former Liverpool striker Fernando Torres led a counter-attack before squaring the ball to substitute Willian for a simple finish.

Chelsea face Atletico Madrid in the second leg of their Champions League semi-final at Stamford Bridge on Wednesday after a goalless initial encounter in Spain.

Despite Sunday's success, Chelsea manager Jose Mourinho insisted either Liverpool or City would end the season as champions of England.

"Now we can say we won both matches against the champions," Mourinho told Sky Sports. "If it's Liverpool, we won both. If it's City, we won both.

"The champions will be City or Liverpool so we have nothing to celebrate," the Portuguese added after making seven changes to his starting side at Anfield.

Liverpool manager Brendan Rodgers, a member of the backroom staff during Mourinho's first spell at Stamford Bridge, bemoaned Chelsea's defensive style.

"There was (were) probably two buses parked today, rather than one," he said.

"It's the style of football, it's a defensive style. It's the polar opposite to how we work."

But Rodgers insisted all was not lost for Liverpool.

"We are still two points ahead of a team (Chelsea) that has spent an absolute fortune.

"If we win our last two games we finish above them and then we'll see what happens with Manchester City."

Earlier on Sunday, Sunderland climbed out of the Premier League relegation zone with a 4-0 win at home to 10-man fellow strugglers Cardiff City.

Connor Wickham headed Sunderland, who kicked off bottom of the table, into a 26th-minute lead at the Stadium of Light but the match took a decisive turn on the stroke of half-time.

Wickham was bearing down on goal when his shirt was tugged by Cardiff centre-back Juan Cala, whose poor back-pass had let him in.

Referee Phil Dowd played an advantage after Wickham stayed on his feet but, when that didn't lead to a goal, the referee blew for a penalty and sent off Cala.

Fabio Borini, as he'd done in Sunderland's shock 2-1 win over Chelsea last week, scored from the spot.

Emanuele Giaccherini put the result beyond doubt before Wickham headed in his second goal four minutes from time.

Sunderland's victory saw Gus Poyet's side move above Norwich, who dropped into the relegation zone on goal difference, and plunged Cardiff to the bottom.

Saturday saw Ryan Giggs launch his reign as interim Manchester United manager following the sacking of David Moyes with a 4-0 home thrashing of Norwich City.

Everton missed the chance to go above Arsenal in the race for fourth position, and a place in next season's Champions League, after two own-goals condemned them to a 2-0 loss at Southampton.

Arsenal will move four points in front of Everton with two games to play if they beat Newcastle United at the Emirates Stadium on Monday.