James Milner's 84th-minute penalty earned Liverpool a gritty 2-1 victory at Swansea City on Saturday that saw Jurgen Klopp's side climb to second place in the Premier League table.
Leroy Fer gave struggling Swansea an eighth-minute lead, but Roberto Firmino equalised early in the second half before Milner claimed the winner following a foul on Firmino by Angel Rangel.
Chelsea ended a three-game winless run with a 2-0 win at Hull City that provisionally lifted Antonio Conte's men to sixth, while a memorable Dimitri Payet goal earned West Ham United a 1-1 draw with Middlesbrough.
James Milner has netted 4️⃣ spot kicks so far this season - more than any TEAM! pic.twitter.com/Cyc3RX9nZV— Premier League (@premierleague) October 1, 2016
Despite Liverpool's fourth straight league success, manager Klopp said: "I was very angry. I have lost a lot of football games, but today makes no sense.
"We were not ready and it is my responsibility. It was not good. The build-up was too static, no movement. We were never compact enough and we lost a lot of balls. We got better in the second half and when we let the ball roll it became difficult for Swansea. The second half was better, but still not brilliant."
Liverpool finished the day two points adrift of leaders Manchester City, who visit third-place Tottenham Hotspur on Sunday.
Fer broke the deadlock at the Liberty Stadium by converting from close range after Borja Baston had knocked down a corner at the back post.
The visitors levelled in the 54th minute, Firmino directing a header into the bottom-left corner from Jordan Henderson's lobbed pass after Philippe Coutinho's free-kick struck the wall.
After Rangel bundled into the back of Firmino, auxiliary left-back Milner chipped his penalty down the middle to condemn Swansea to a fifth defeat in six games, piling the pressure on manager Francesco Guidolin.
Beaten by Liverpool and Arsenal in their previous two games, Chelsea bounced back with a 2-0 success over Hull at the KCOM Stadium.
Brazilian winger Willian and Spain striker Diego Costa scored Chelsea's goals inside six second-half minutes, both players curling shots into the bottom-right corner.
Conte's men drew level on points with fifth-place Arsenal, who visit Burnley on Sunday.
"It's an important win after two defeats," said Conte.
"This win is important for the team because we are working hard. After two defeats it's not easy because you must work and also find the resolution to change and to improve."
France international Payet further endeared himself to West Ham's fans with a sensational equaliser against Boro to prevent Slaven Bilic's team succumbing to a fifth straight league defeat.
Cristhian Stuani headed Boro in front early in the second half, but West Ham levelled in the 57th minute when Payet waltzed across the box from the left, beating five defenders, before drilling home.
Watford and Bournemouth played out an entertaining 2-2 draw at Vicarage Road.
Patrick van Aanholt's 83rd-minute equaliser earned Sunderland manager David Moyes a measure of respite in a 1-1 draw at home to West Bromwich Albion, who had gone ahead through Nacer Chadli.