Mane header at the back post, off a flawless Roberto Firmino cross, put Jurgen Klopp's men in front in the 51st minute before Salah rifled in a long-range effort to the top left corner to double their lead two minutes later. City's result would have punctured belief, Liverpool aware no matter how long they extend their winning streak they are running out of games.
Chelsea dented Liverpool's title push with a 2-0 victory at Anfield in the 2013-14 campaign but Sarri warned his third-placed team that they could face a daunting task on Sunday. In a twist of fate, City played Palace that day, too.
Chelsea, who started the season in excellent form, are in a battle to hold off Arsenal and Man Utd in a battle for 4th place and the lucrative involvement in the Champions League.
The clearest chance of a lively first half fell to Mane in the 38th minute but the Senegalese forward fired high and wide from Salah's cutback.
The German lauded the energy of his front three and how Liverpool's midfield dealt with Jorginho, although there are concerns for Jordan Henderson, who picked an ankle knock.
As is going to be the case for every game between now and the end of the season, nothing less than a win was going to cut it for Liverpool in this one.
After today, the Reds take on Cardiff, Huddersfield, Newcastle United and Wolves as they go in search of their first Premier League title.
"We controlled the ball really well but one moment in the game and they are back in it", Sterling said."But we responded again and got the third goal". We only try to collect as many points as possible.
City's season concludes with games against Burnley, Leicester and Brighton.
It was as manic a couple of minutes as those which saw Liverpool take a lead and quickly double it just after half-time.
"We are fighting to be champions back to back". They won here back in September to knock the reds out of the League Cup.
Former Liverpool player Sterling said he felt the title race would go to the final match."The way Liverpool have been playing it will go down to the wire". So we will see.
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