Tottenham beat Aston Villa on Sunday to ease the pressure on manager Nuno Espirito Santo as Liverpool and Manchester City prepared to lock horns at the top of the Premier League.
Elsewhere, Leicester City let a 2-0 lead slip at Crystal Palace to draw 2-2 while new boys Brentford scored deep into stoppage time to beat West Ham 2-1.
Tottenham were surprise early pacesetters this season but three straight defeats with an aggregate score of 9-1 sent them tumbling down the table.
Former Wolves boss Nuno was not first choice to replace Jose Mourinho in the close-season and there have already been murmurings that Tottenham's players are bored of his training methods.
But Sunday's 2-1 home win against in-form Villa will buy the Portuguese boss some breathing space as players head into the international break.
Spurs looked shaky again when Ollie Watkins cancelled out Pierre-Emile Hojbjerg's first-half opener but a Matt Targett own goal in the 71st minute proved decisive.
The win lifts Spurs to eighth in the Premier League table, two points outside the top four.
"Good, good, good," Nuno told Sky Sports. "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, who have grown used to life near the top of the table in recent seasons, 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 six minutes later.
Palace got 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.
Liverpool will kick off their match against City at Anfield second in the Premier League, one point ahead of the defending champions.
The two teams have dominated the English top-flight in recent years, with City winning the title in three of the past four seasons and Liverpool finishing top of the pile in 2020.
Chelsea and Manchester United have been talked up as title contenders this season after spending big in the transfer market.
But Klopp believes City remain the team to beat as they showed in a 1-0 win at Chelsea last weekend, which was more convincing than the scoreline suggests.
"They are still really, for me, probably the best team in Europe in the moment and it's a tough one," said Klopp.
"Last weekend, they played Chelsea and everybody was talking about Chelsea, how good they are –- and they are good, oh my God, they are really good -– but City was clear, clear better that day."
City boss Pep Guardiola said his personal duels with Klopp have made him a better manager.
In 21 meetings between the pair, both have won nine with three draws.
Earlier Sunday, Watford announced the sacking of head coach Xisco Munoz after a poor start to the Premier League season.