The trio all found the net to condemn Arsenal to a second successive defeat after their 1-0 loss at Stoke City.
The trio all found the net to condemn Arsenal to a second successive defeat after their 1-0 loss at Stoke City, leaving them six points below early Premier League pace-setters Manchester United in 16th place.
Liverpool rose to second place, two points below United and one above champions Chelsea, who recorded a straightforward 2-0 win over Everton.
"We were really well organised," said Liverpool manager Jurgen Klopp.
"If you give Arsenal space and time, you lose before the game starts, so I don't think they could do a lot of what they wanted, Arsenal, and that is all credit to the boys because they worked really hard."
Tottenham Hotspur are two points further back in ninth place after their Wembley hoodoo resurfaced in a 1-1 draw at home to Burnley.
Arsenal's defeat, and the toothless manner of their surrender, will once again raise questions about Wenger's position, less than three months after the Frenchman signed a new two-year contract.
It was Arsenal's heaviest league defeat since a 4-0 loss at Southampton in December 2015.
"Mentally it was difficult," Wenger told Sky Sports. "A very disappointing performance. It was disastrous."
"The result is a consequence of the performance. It was not good enough. We were beaten everywhere physically and in the end we made it easier for them."
Wenger was able to hand Alexis Sanchez his first start of the season after an abdominal strain, but saw his side fall behind in the 17th minute when Joe Gomez crossed from the right for Firmino to head home.
Firmino turned provider in the 40th minute with a pass down the left to Mane, who cut inside Rob Holding before drilling a shot into the bottom-right corner.
It was 3-0 before the hour as Liverpool cleared a corner and Salah beat Hector Bellerin to a bouncing ball midway inside his own half before sprinting clear to tuck a shot past Petr Cech.
Sanchez, who has been strongly linked with a move away, was taken off just after the hour and looked a picture of misery as he took his seat on the bench, sinking his head between his legs.
Substitute Daniel Sturridge completed the scoring by heading in a cross from Salah in the 77th minute.
Tottenham have now won just once in 11 games at the new Wembley after following up last weekend's 2-1 loss to Chelsea with a frustrating draw against Burnley.
Dele Alli put Spurs ahead in the 49th minute after Burnley failed to clear a corner, but new striker Chris Wood earned Sean Dyche's men a share of the spoils in stoppage time by applying a cool finish to Robbie Brady's fine pass.
"We had the chance to score a second or third, but we missed," said Spurs manager Mauricio Pochettino. "Sometimes you pay."
Alvaro Morata scored one goal and made another as Chelsea returned to winning ways at Stamford Bridge with a routine win over previously undefeated Everton.
Stunned 3-2 by Burnley in their opening home game, Chelsea took a 27th-minute lead when Cesc Fabregas steered a shot into the bottom corner from Morata's knock-down.
Morata scored his second Chelsea goal five minutes before half-time, emphatically converting Cesar Azpilicueta's cross with his head.
"We played a really good game," Chelsea manager Antonio Conte told the BBC.
"The only negative thing is we should be more clinical."
West Bromwich Albion's 100 percent record came to an end as they were held to a 1-1 draw by Stoke City at The Hawthorns.
Jay Rodriguez's diving header put West Brom in front just beyond the hour, but Stoke levelled 13 minutes from time when a miscued clearance by Ahmed Hegazi enabled substitute Peter Crouch to head into an empty net.