Just for good measure, his assist for Virgil van Dijk's second-half goal, which confirmed all three points, was his fifth in the league.
It was Liverpool who looked most like adding to the scoring in stoppage time, though, with Salah refusing to give the Wolves defence any respite as he first forced another save from Patricio before catching Willy Boly in possession and teeing up Georginio Wijnaldum, who fired when when he really should have scored.
Eight of the last nine champions in the Premier League were in first place at Christmas.
After taking the lead, the lads from London were too good and romped away thanks to some excellent football and really bad defending from Marco Silva's team.
He said: "If you want to do the headline "Klopp says we need 105 points to win the title" then do it".
Despite feeling under the weather, Van Dijk made himself available for the match to ease Jurgen Klopp's defensive crisis, with Joe Gomez, Joel Matip and Trent Alexander-Arnold all out injured for the start of the busy festive period. Exceptional. It wasn't ever such a tight race.
"So far it looks like a really special season, 48 points before Christmas is insane", Klopp said.
Chelsea enjoyed a 12-game unbeaten streak at the start of the season, but defeats at Tottenham and Wolves saw them slip behind Liverpool and City. "One of the most hard games of the season and we won it".
Van Dijk overcame illness to deliver an outstanding performance against Wolves that earned the acclaim of his manager and former Liverpool defender Jamie Carragher.
His finish against Wolves was classy, meeting Fabinho's low cross from the right byline with a first-time flick with the outside of his left foot.
After the game with Wolves, Klopp hailed Van Dijk for his assured display and claimed that he thinks he is an even better player than he thought. A corner was cleared as far as Salah, who delivered a teasing cross from which Van Dijk stretched to turn the ball home. Klopp, however, believes that Liverpool may need to improve on that record in the second half of a season that he described as "exceptional".