With City not in action until the derby against Manchester United today, Liverpool took the chance to increase the pressure on the champions.
Mane netted in the 27th minute at Anfield with a close-range finish from Trent Alexander-Arnold’s cross.
The Senegal forward’s goal survived a VAR check for offside and that was all Liverpool needed to make it seven successive league wins.
Even if City beat United, Liverpool have a game in hand to keep the leaders within touching distance as they chase an unprecedented quadruple.
“I don’t know if we will remember this game as one of the important ones,” said Liverpool boss Jurgen Klopp after West Ham missed a number of chances to take a point.
“If you are not well organised you have to defend with passion and that’s what we did.”
Defeat was a blow to fifth-placed West Ham’s hopes of finishing in the top four, leaving them two points behind fourth-placed Manchester United.
All Premier League captains were wearing armbands in Ukraine colours this weekend and clubs held a minute’s applause in a show of solidarity with the country following Russia’s invasion.
The war has indirectly taken a major toll on Chelsea, with Russian oligarch Abramovich putting the club up for sale amid fears he may be sanctioned by the British government for his alleged links with Russian President Vladimir Putin.
Abramovich’s vast investment delivered 19 major trophies in his 19-year reign, including the Champions League and Club World Cup under Tuchel.
But Tuchel felt a section of Chelsea’s support went too far before their 4-0 win at Burnley when they chanted Abramovich’s name during the Ukraine applause.
“It’s not the moment to do this,” Tuchel said. “If we show solidarity we show solidarity. As a club we need our fans to commit to this minute of applause.
“We do it for Ukraine and there is no second opinion about this situation. We should stand together.”
Qualifying for the Champions League is Tuchel’s main aim regardless of the Abramovich drama and third-placed Chelsea remain on course after brushing aside third-bottom Burnley.
Reece James put them ahead in the 47th minute with a fierce finish and Kai Havertz struck with a header five minutes later.
Havertz made it three goals in nine minutes with a close-range strike from James’ cross.
Christian Pulisic tapped in Chelsea’s fourth in the 69th minute from Saul Niguez’s deflected cross.
Chelsea’s third successive league win moved them six points clear of Manchester United.
Leeds beaten on Marsch bow
Jesse Marsch has been hired to save Leeds from relegation after replacing Marcelo Bielsa.
But Marsch was unable to spark an immediate improvement in their fortunes as Harvey Barnes’ 67th minute goal gave Leicester a 1-0 win.
Leeds have lost their last five games and sit just two points above the relegation zone.
“We are getting to know each other. To play so well at a tough place, it doesn’t feel right that we didn’t get what we deserved but that’s sport. A big first step for us,” Marsch said.
Ivan Toney’s hat-trick lifted Brentford to their first win in 10 league games as the Bees moved six points clear of the relegation zone with a 3-1 victory at bottom-of-the-table Norwich.
Christian Eriksen provided the assist for Toney’s opener in his first competitive start since suffering a cardiac arrest playing for Denmark at the last year’s European Championship.
Newcastle extended their unbeaten run to eight league games with goals from Ryan Fraser and Fabian Schar clinching a 2-1 win against Brighton at St James’ Park.
In severe relegation trouble when Eddie Howe took over as manager, Newcastle are now seven points above the bottom three.
Aston Villa thrashed Southampton 4-0 thanks to goals from Ollie Watkins, Douglas Luiz, Philippe Coutinho and Danny Ings.
Jean-Philippe Mateta and Wilfried Zaha scored in Crystal Palace’s 2-0 victory at Wolves.