Liverpool came from behind to beat Swansea 2-1 and go second in the Premier League overnight as Chelsea picked up a much-needed victory with a 2-0 success at Hull.
James Milner's late penalty lifted Liverpool up three places to within two points of leaders Manchester City.
Swansea took an early lead at the Liberty Stadium through Leroy Fer but Roberto Firmino equalised for the visitors in the 54th minute.
Milner then struck from the spot for the fourth time this season in the 84th minute after Firmino was fouled by Angel Rangel.
"We are really happy in this moment," Liverpool manager Juergen Klopp said after his team's fourth straight league win.
"In the second half we bossed them - it's how we should have been. We asked more difficult questions.
"You need to show every week that you ready to fight for the result. We did it in this game."
The defeat will keep pressure on Swans manager Francesco Guidolin, whose side have lost five of their last six in the league and sit just above the relegation zone.
"My team played a very good game, Liverpool is a very strong team," he said. "The draw would have been the right result."
Chelsea steadied their ship after two straight losses.
Willian put the Blues in front in the second half and Diego Costa clinched the three points with his league-best sixth goal.
West Ham avoided a fifth straight loss with a 1-1 home draw against Middlesbrough. Dimitri Payet cancelled out an opener from Boro's Cristhian Stuani at the London Stadium.
West Ham remain winless in five and in the bottom three on goal difference behind Swansea.
Winless Sunderland moved off the bottom of the table with a 1-1 home draw against West Brom.
Substitute Patrick van Aanholt's goal seven minutes from time lifted the Black Cats above Stoke on goal difference.
Watford twice came from behind to draw 2-2 with Bournemouth with Isaac Success netting the second equaliser.
Manchester City look to make it seven wins from seven when they visit Tottenham, Manchester United host Stoke, champions Leicester take on Southampton and Burnley welcome Arsenal in Sunday's games.