Liverpool s Brazilian midfielder Fabinho (C) celebrates scoring the opening goalduring the English Premier League football match between Burnley and Liverpool at Turf Moor in Burnley, north west England on February 13, 2022 (AFP)
Fabinho struck late in the first half at windswept Turf Moor to give Liverpool their fourth successive league victory.
Liverpool are nine points behind City with one game in hand as the Reds refuse to let the title race become a prolonged coronation for Pep Guardiola's men.
City made it 14 wins from their last 15 league games on Saturday as Raheem Sterling's hat-trick inspired a 4-0 win at lowly Norwich.
But Guardiola is convinced Liverpool will push the champions all the way to the finish line and the way they ground out a hard-fought success against bottom of the table Burnley suggests he is right not to count them out.
"It is nine points and then it is 12 points because most of the time City play before us. These are really difficult games. That is why we don't think about the title race," Reds boss Jurgen Klopp said.
Klopp was able to welcome back Sadio Mane for his first appearance since helping Senegal win the African Cup of Nations.
Burnley were in typically aggressive mood, with Alisson Becker forced to save Josh Brownhill's swirling strike before Wout Weghorst wasted a golden opportunity for the hosts.
After a shaky start, Fabinho restored order for Liverpool five minutes before half-time.
The Brazilian poked home a fifth goal in his last seven games after Mane headed on Trent Alexander-Arnold's corner.
"A perfect afternoon. Raining and windy," Klopp said. "Everything today was set up to be a banana skin for us.
"The balls in the air were so tricky to defend because the wind came from all directions. We played the circumstances rather than suffered from them."
- Spurs implode -
In north London, Tottenham lost a second successive home game as Wolves followed Southampton's victory on Wednesday.
Antonio Conte's side, loudly booed off at full-time, dropped to eighth place, four points adrift of the Champions League places.
"We created chances but in the end we are talking about another defeat. We have to work and to know it won't be easy for us. It's difficult to explain the way we started," Conte said.
Raul Jimenez gave Wolves the perfect start in the sixth minute, the Mexican volleying home after Tottenham keeper Hugo Lloris weakly spilled Leander Dendoncker's effort.
If that was an ugly goal to concede, there was worse to come for Tottenham as they imploded in the 18th minute.
Lloris was involved again with a woeful pass to Ben Davies, prompting the startled defender to gift possession to Wolves.
Daniel Podence's shot was deflected onto the post by Davinson Sanchez and Dendoncker bundled in from close-range.
Wolves, who climbed one point above Tottenham into seventh, have won four successive top-flight away games for the first time since 1980.
Newcastle boosted their survival bid as Kieran Trippier's free-kick clinched a 1-0 win against Aston Villa at St James' Park.
The Magpies, winners of three consecutive league matches for the first time since 2018, are four points above the relegation zone.
Eddie Howe's side were given a penalty when Calum Chambers brought down Joe Willock, but referee Craig Pawson changed his decision after VAR showed the foul took place just outside the area.
It was only a temporary reprieve for Villa as Trippier smashed the resulting free-kick past Emiliano Martinez in the 35th minute for his second set-piece goal in successive games.
Villa were denied a 61st minute equaliser by the slenderest of offside decisions as VAR chalked off Ollie Watkins' far post header.
"It was a tight game and in weeks gone by we wouldn't have won it. We defended heroically but I feel we have a lot to do still," Howe said.
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