Manchester City twice came from behind to draw 2-2 against Liverpool in a thrilling match between the Premier League title rivals on Sunday as Tottenham won to ease the pressure on Nuno Espirito Santo.
Mohamed Salah appeared to have won the game at a frenzied Anfield after Phil Foden had cancelled out Sadio Mane's opener but Kevin De Bruyne's late deflected shot rescued a point for Pep Guardiola's men.
Unbeaten Liverpool are a point behind leaders Chelsea while City are in third place, two points off the top.
Earlier, Spurs beat Aston Villa 2-1 and Leicester drew 2-2 at Crystal Palace while new boys Brentford scored deep into stoppage time to beat West Ham 2-1.
City's dropped points against Southampton last month looked potentially costly, with tricky away matches to come against European champions Chelsea and Liverpool.
But the defending champions have shown their mettle with a 1-0 win last week at Stamford Bridge and now an impressive performance at the home of their fiercest rivals.
City dominated the first half on Sunday but had nothing to show for their endeavours against a lacklustre home team.
City levelled through Foden's drilled finish from an acute angle but Salah produced a sensational solo effort to fire Liverpool back in front in the 76th minute.
The visitors dug deep again and De Bruyne equalised five minutes later with a finish from the edge of the area, which deflected in off Joel Matip.
"What a game," Guardiola told Sky Sports. "That is the reason the last years Man City and Liverpool were always there because we try to play in this way. Unfortunately we couldn't win -- but we didn't lose.
"That's why the Premier League is the best. It was great, really great."
Klopp was disappointed with his side's first-half display but said they turned things around after the break.
"Thank God a football game has two halves," he said. "We are really happy about the second and not so happy about the first for obvious reasons."
"I was most happy in my career about the half-time whistle," he added. "It was never planned that we played like this and we needed half-time and we used half-time and played a really good second half."
- Spurs win -
Earlier, Tottenham beat in-form Aston Villa 2-1 to end a painful run of three straight league defeats, buying Portuguese manager Nuno some breathing space as the players head into the international break.
Spurs were surprise early pacesetters this season but those losses with an aggregate score of 9-1 sent them tumbling down the table.
Spurs wobbled when Ollie Watkins cancelled out Pierre-Emile Hojbjerg's first-half opener but a Matt Targett own goal in the 71st minute proved decisive.
"Good, good, good," Nuno said. "We needed a win but a well-deserved win. We did a good match against tough opponents.
"Important for us, the boys and the fans. We reacted well after conceding and positive in a lot of ways."
Leicester travelled to Selhurst Park without a Premier League win since August.
Crystal Palace dominated the early exchanges but the visitors snatched the lead through Kelechi Iheanacho just after the half-hour mark and Jamie Vardy doubled the lead.
Palace pulled a goal back on the hour, with substitute Michael Olise firing past goalkeeper Kasper Schmeichel at the second time of asking and fellow substitute Jeffrey Schlupp headed the home side level.
Across London, Bryan Mbeumo put Brentford in front against West Ham only to see his effort cancelled out 10 minutes from full-time by Jarrod Bowen.
But replacement Yoane Wissa had the final say when he blasted home in the 94th minute after the hosts failed to clear from a Mathias Jensen free-kick.
Earlier Sunday, Watford announced the sacking of head coach Xisco Munoz after a poor start to the season.