Richard Stearman put the visitors ahead after only 53 seconds, left unmarked to head in Helder Costa's free-kick.
Costa then set up Andreas Weimann to
round Liverpool keeper Loris Karius and double Wolves' lead before the break.
Divock Origi scored late on to set up a frantic finale but a largely subdued Liverpool failed to find an equaliser.
The result is the second defeat in cup competition in four days for Jurgen Klopp's side after they lost to Southampton in the EFL Cup semi-finals on Wednesday, and a third home defeat in a week.
Wolves' second straight victory over Premier League opposition in the FA Cup sees them reach the fifth round for the first time since 2008.
Groundhog Day in January
Liverpool have now won just one game in eight in January, with the Reds reliving recent mistakes as they failed to break down an organised team while also showing crippling defensive frailty.Their weakness at the back was exposed inside the first minute, the hosts conceding a free-kick on right for the left-footed Costa to swing in a dangerous cross, with Origi and Georginio Wijnaldum failing to pick up Stearman, who easily headed in at the back post.
The other symptom of Liverpool's January blues was also apparent as they dominated territory and possession but could not unpick a well-drilled Wolves defence, the previously free-scoring Reds having managed only six goals in those eight games.
Indeed, it took until 59 minutes for the hosts to have a shot on target, substitute Philippe Coutinho drawing a straightforward save from Wolves' 20-year-old goalkeeper Harry Burgoyne, making only his third senior appearance.
Trying to find some attacking fluency, Klopp also sent on Daniel Sturridge, with the England striker showing composure to steer the ball back across the box late on for Origi to fire in, but it ultimately proved in vain.
With another meek exit from a major competition, Liverpool's season now looks in danger of completely unravelling, with all hopes pinned on the Premier League as a crucial match against leaders Chelsea beckons on 31 January.
Classy Costa catches Reds on the counter
If Wolves' first goal was a targeted attempt to terrorise Liverpool at set-pieces, the second was an exquisite example of how to catch out an inexperienced defence on the counter-attack.Wolves defender Matt Doherty played a quick pass up to Costa after yet another Liverpool attack broke down, the Portuguese racing away and holding off Alberto Moreno to slip in Weimann, who showed a deft touch to calmly round Karius and score.
The hosts even had advance warning of both Wolves' counter-attack capabilities and Costa's pace after the on-loan Benfica winger had surged from his own area on a brilliant run, only to scuff his shot.
As a point of comparison, when Liverpool had their own chance to break with numbers, left-back Moreno played a woeful pass straight to a Wolves defender with Origi clear through.
Wolves boss Paul Lambert is keen to make Costa's loan move permanent yet the 23-year-old may have other suitors after an impressive display.
Lambert's turnaround gathers pace
When Lambert took over at Molineux in November following the sacking of Walter Zenga, Wolves were 19th in the Championship and three points above the relegation zone.Although their league position has only improved by one place, they are now seven points clear of the drop, with this their sixth win in Lambert's 13 games in charge and second against a Premier League side after victory at Stoke in the third round.
For long periods, Wolves executed a press that Klopp would be proud of, while they were resolute in defence led by on-loan Fulham defender Stearman, who also played in the visitors last victory at Anfield, a 1-0 win in December 2010.
That organisation, coupled with the pace of Nouha Dicko and Costa up front should make Wolves a tough proposition for whoever they draw in the fifth round.
Man of the match - Helder Costa (Wolves)
'We'll enjoy the ride' - manager reaction
Wolves manager Paul Lambert said: "I think from the off we started well and counter-attacked. We pressed when we had to press and sat back when we had to be compact. The gameplan was brilliant."[The last few minutes] it was horrible. I'm happy to admit that. The lads were running on empty. I've been here a few times before and this is the best result for me.
"We'll enjoy the ride. We might get dismantled in the next game but the last two games have been unbelievable."
Liverpool manager Jurgen Klopp said: "I am responsible for this performance because I thought this line-up was ready for this game but obviously we weren't and that doesn't feel too good.
"I could look for excuses but I don't want to, maybe we should use this time to be disappointed, to be frustrated, to be angry at ourselves.
"All I can say. Sorry."
Liverpool's poor run of threes - match stats
- Liverpool have lost three consecutive games at Anfield for the first time since October 2012 (under Brendan Rodgers).
- Jurgen Klopp has suffered three consecutive home defeats as a manager for the first time since April 2007, while in charge of German side FSV Mainz.
- Liverpool's past three FA Cup defeats at Anfield have all been to second-tier sides (Barnsley 2008, Reading 2010, Wolves 2017).
- Andreas Weimann has scored in three of his past four appearances at Anfield (two for Aston Villa and one for Wolves).
- Helder Costa has been directly involved in 11 goals in his past 11 games in all competitions for Wolves (five goals, six assists).
- Richard Stearman netted his first goal in any competition since April 2014, 1,013 days ago (for Wolves v Leyton Orient).