VAR took centre stage on Merseyside as it interfered with two goals in the first half, awarding one and disallowing the other.
Sadio Mane thought he'd given Liverpool the lead on 42 minutes but the referee had blown for a handball on Adam Lallana.
A lengthy VAR check eventually awarded the goal as replays showed it touched his shoulder and not his arm, a fine example of how the technology can work.
Soon after, though, Wolverhampton Wanderers had thought they'd equalised through Pedro Neto and celebrations were well underway until it was ruled out for a tight offside call in the build up.
Story of the game
The opening stages of the first half were relatively quiet at Anfield as Liverpool dominated possession and looked to push for an opener.
Three minutes in Trent Alexander-Arnold sent in a pin-point cross and put it on a plate for Mohamed Salah, but his effort flew over the bar.
On six minutes, a rare mistake from Virgil Van Dijk left Joe Gomez in a foot race with Neto and conceded the Reds' first corner of the game.
Salah attempted a one-two with Lallana and nearly put the Reds ahead with 11 minutes gone, denied only by two defensive blocks from the Wolves backline.
The flag eventually went up as the Egyptian strayed just offside in the build-up but it was a well-worked Liverpool move.
A few minutes later, a quick corner from the hosts carved an opportunity as most people switched off - all except Georginio Wijnaldum who picked the ball up in the box and put a good chance over the bar.
Midway through the first half Van Dijk sent a fantastic ball through to Mane, who layed it off to Salah.
It dropped kindly for the Egyptian on the volley but his effort was comfortably held by the Wolves keeper.
30 minutes in, Mane spun to get a shot away but his attempt was deflected wide. The resulting corner saw Roberto Firmino head just wide of the post.
It took until the closing stages of the first 45 for Liverpool to find a breakthrough.
Mane gave the Reds the lead with a drilled effort into the bottom corner, but Anthony Taylor blew for a handball in the build up because of Lallana.
Replays showed the midfielder used his shoulder as opposed to his arm. A long VAR check eventually gave the goal, much to the visitor's frustrations.
Anger surfaced and Wolves piled on the pressure, eventually going level in stoppage time.
Neto stunned Anfield as Liverpool failed to clear a corner effectively and he fired an effort past Alisson.
Tensions were high as VAR looked at the position of Jonny in the build up and eventually deemed the goal to be offside, a decision that saw manager Nuno Espirito Santo booked for voicing his disapproval.
It was early changes in the second half for the Wolves coach as Adama Traoré and Romain Saiss came on for Ruben Neves and Leander Dendoncker.
Liverpool continued to pile on the pressure, though, as moments later Firmino sent an effort off-target following some good build-up from Salah and Mane.
There were shouts for a penalty with 64 minutes gone as Mane was closed down and brought down in the box as he tried to get a shot away, it was deemed a fair challenge and the referee waved play on.
Lallana's evening came to a close just after as he made way for Naby Keita, with just under half an hour left to play.
Alisson bailed out Van Dijk with a save at his near post to deny Diogo Jota, the central defender appeared far to casual on the ball as he was dispossessed in a dangerous position and conceded a good opportunity.
Raul Jiminez then took the place of Jota on 71 minutes, being Wolves' third and final substitution.
A dangerous break with 10 minutes to go saw Salah nearly extended the Reds' lead.
A heavy touch allowed Conor Coady to step in and prevent a clear cut opportunity.
Jiminez scuffed a good chance on 82 minutes as he fired an effort over the bar, swiftly closed down by both Alexander-Arnold and Gomez.
It was a double change for Liverpool on 85 minutes as Wijnaldum and Firmino made way for Divock Origi and James Milner - the game very much on a knife edge.
Wolves found themselves with two late opportunities on the edge of the box, but hurried their efforts and sent them flying over the bar - huge let-offs for Liverpool as some lacklustre defending conceded the chances.
Ruben Vinagre was next to let a late chance go begging as he attempted a shot from a tight angle, sending it off target after beating Alexander-Arnold in the build up.
A vital block from Van Dijk deep into stoppage time to deny a Traoré effort proved to be enough to ensure Liverpool's cloak of invincibility remained firmly in tact as they earned another three points.
Takeaways from the match
VAR causes debate, yet again...
It wasn't the most entertaining game on the pitch as both teams appeared to struggle for energy, which is understandable given the intense fixture schedule.
But, there were plenty of talking points surrounding VAR and the decisions made in the first half.
The technology was used at its best 42 minutes in surrounding Liverpool's opener - although Wolves' players remained aggrieved complaining about a earlier hand ball officials deemed 'inconclusive.'
A large number of goals have been disallowed this season for tight offside calls, Wolves' equaliser can be added to the list.
Liverpool themselves have been on the wrong end of similar decisions, Mane against Watford and Firmino against Aston Villa the situations that come to mind.
Van Dijk's 100th appearance...
The Dutch defender wasn't at his best as he made his 100th appearance for the Reds.
Both Gomez and Alisson were called into action across the 90 minutes to bail the 28-year-old out of uncharacteristic mistakes.
Of course though, with such high standards set for himself, even the slightest drop off is noticeable.
Though it was his late last-ditch defending deep into stoppage time that secured the three points for Liverpool - so even his "off days" are still solid enough performances.
Another tough fixture, another win...
Once again Jurgen Klopp's side have forced themselves over the line and navigated their way through a difficult fixture.
Wolves walked into Anfield bouncing after a fantastic comeback to beat Manchester City only a few days ago, and carried on that form by putting in a resilient yet dangerous display against Liverpool.
Wolves isn't an easy game for any side, but once again the 'mentality monsters' saw the game out and extended their unbeaten run, ending 2019 with an important victory.