Jurgen Klopp sent out an attack-minded line-up and was rewarded with a scintillating 4-3 win at a jubilant Anfield, where the emotions were in sharp contrast to Wenger’s misery after a 2-1 loss at struggling Bournemouth.
At Anfield, Alex Oxlade-Chamberlain’s early strike was cancelled out by Leroy Sane’s goal shortly before half-time but three goals in nine scintillating minutes stunned Pep Guardiola’s men.
Two late goals gave City hope but they fell just short in their desperate bid to keep their unbeaten run going.
The result means that City remain 15 points clear of second-placed Manchester United at the top of the Premier League table ahead of United’s match at home to struggling Stoke on Monday. Liverpool leapfrog Chelsea into third spot.
Klopp’s side, in their first match since Philippe Coutinho left to join Barcelona, showed they still have enviable depth in attack, taking the lead in the ninth minute when Oxlade-Chamberlain marauded forward and thundered a shot past City stopper Ederson.
The home side held onto their lead until five minutes before half-time, when Leroy Sane gathered a raking cross-field ball from Kyle Walker and beat Loris Karius at his near post with a rasping left-foot shot that the Liverpool keeper should have saved.
Guardiola’s team looked in control after the break before Liverpool’s goal glut.
Roberto Firmino dinked a clever shot in off the post following a through-ball by Oxlade-Chamberlain and just two minutes later Sadio Mane smashed a shot into the top corner to make it 3-1.
With City rocking, Mohamed Salah scored Liverpool’s fourth with a left-footed shot from more than 35 yards out after Ederson had misplaced a clearance.
City scored late through Bernardo Silva and Ilkay Gundogan but ran out of time in their search for a dramatic equaliser.
Earlier, Arsene Wenger left Chile international Sanchez out of his squad to travel to Bournemouth as transfer speculation swirls over a potential move to Manchester City or Manchester United.
“Alexis would have played,” said Wenger, after Arsenal leaked two goals in four second-half minutes to slip to defeat.
“Alexis would have played, but it’s a difficult period for him. He’s always been committed until now but he could have gone yesterday and he could go in the next 48 hours.”
Wenger, who said Sanchez had not refused to play, added that he would be replaced if he left.
City remained favourites to sign the Chile international this month until Manchester United expressed their interest last week.
The Old Trafford club’s willingness to meet Arsenal’s £35 million valuation of Sanchez, who can leave as a free agent at the end of the campaign, together with the possibility of offering one-time Arsenal target Henrikh Mkhitaryan as part of any deal, has increased the chance of the forward joining Jose Mourinho’s squad.
Arsenal have lost their past three Premier League games in which Sanchez has not played any part, showing how much they will miss the forward when he leaves the club.
On Saturday, 10-man Leicester held Chelsea to a 0-0 draw at Stamford Bridge while Tottenham put Everton to the sword, with Harry Kane scoring twice in a 4-0 rout.