The Reds - who have now won seven league games in a row - move four points clear of Manchester City at least until tomorrow, when the defending champions take on Crystal Palace at the Etihad Stadium.
Wolves were gifted a chance to break the deadlock after only four minutes when Fabinho's sloppy pass was picked off and fell to Adama Traore, who fired an early shot wide of the near post rather than trying to take on Van Dijk.
The same two came up against each other again in the 10th minute as Wolves' counter-attacking game plan almost paid off when Raul Jimenez released Traore, but once again Van Dijk stood his ground and the speedy Wolves attacker could only drill wide.
It was the home side that looked most like scoring in the opening quarter of an hour and the sodden conditions almost came to their aid shortly afterwards when Romain Saiss's deflected effort was spilled into a dangerous area by Alisson Becker, who was fortunate to see Fabinho there to clear the danger.
A touch of class from Salah made the difference in the first half, though, as Liverpool took the lead with their first real chance of the contest.
The Egyptian winger saw his initial free kick come to nothing, but carried his run on into the box and impudently flicked his finish past Rui Patricio with the outside of his foot after Fabinho had exchanged passes with Sadio Mane and cut the ball back.
The goal saw Salah move out on his own as the league's top scorer, and it also took the wind out of the home side's sails as they struggled to rediscover their attacking impetus after falling behind.
James Milner drew one save from Patricio with a left-footed piledriver before Wolves did begin to grow back into the game towards the end of the half, with Jonny Castro testing Alisson with a low strike which the keeper held well in the difficult conditions.
Liverpool briefly responded when Salah nudged Naby Keita's cross towards goal, but it was Wolves who ended the half on top and Matt Doherty pounced on a short pass from Keita before forcing another stop from Alisson.
It was far from a vintage performance from Liverpool despite going into the break ahead, but they looked far more comfortable in the second half and almost doubled their lead within three minutes of the restart when Salah's half-volley flew over the bar.
There was a blow for the visitors shortly before the hour mark when Keita was forced off with an injury, but his replacement Adam Lallana was thwarted by a good block just moments before Liverpool doubled their lead.
Van Dijk, who had provided another dominant display at the back, made his mark at the other end of the field with his first league goal for the club, latching on to Salah's exquisite cross and cushioning his volley past Patricio.
Wolves almost produced an immediate response to drag themselves back into the game when a mini-goalmouth scramble ended with the ball falling to Saiss, but his snapshot was straight at Alisson.
The hosts have taken points off Manchester City, Chelsea, Arsenal and Manchester United already this season, but they looked short of ideas in the second half and Liverpool almost added a third when Patricio thwarted Salah from a tight angle before Mane nodded off target from the resulting corner.
There was one glorious chance for Wolves to set up a nervy finale late on when the ball struck Andrew Robertson's heel inside the area and fell kindly for Morgan Gibbs-White, but the Wolves sub could only pick out the side-netting with his finish.
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.
It proved to be the final action of the match as Liverpool ensured top spot at Christmas - a position from which nine of the last 10 occupants have gone on to win the title from.
The Reds also extend their club-record unbeaten run to 19 Premier League games ahead of their Boxing Day clash with Newcastle United, while Wolves see their three-match winning streak come to an end and will face Fulham on Boxing Day.
WOLVES (3-4-1-2): Patricio; Bennett, Coady, Boly; Doherty, Neves, Saiss, Jonny (Vinagre 81'); Moutinho (Gibbs-White 63'); Jimenez, Traore (Cavaleiro 63')
LIVERPOOL STARTING XI (4-3-3): Alisson; Milner, Lovren, Van Dijk, Robertson; Henderson, Fabinho; Mane (Clyne 87'), Firmino (Wijnaldum 76'), Keita (Lallana 58'); Salah body check tags ::