Holders Liverpool were undone by two defensive blunders that allowed Wolves to claim a 2-2 draw and a replay from their FA Cup third-round tie at Anfield on Saturday.
A disjointed Liverpool looked to have recovered from Alisson's early gift to Goncalo Guedes to give Wolves the lead when Darwin Nunez and Mohamed Salah scored either side of half-time.
But more poor defending from Jurgen Klopp's side allowed substitute Hwang Hee-Chan to give the team 19th in the Premier League a deserved replay at Molineux later this month.
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"It was a good start, a dominant start," Klopp told ITV. "We played really good football moments and then we concede. The goal should not happen, but we all know how often Ali [Alisson] saves our backsides.
"They had counter-attacks before then, it is always dangerous when [Adama] Traore gets the ball. We could see that. We came back with a fantastic equaliser, everything was clear at half-time what we wanted to improve and change to cause them more problems.
"Then it was a dominant performance before they got a foot in the game and we didn't win enough challenges from there. They caused us massive problems. We kept the problems in the game. The equaliser was unlucky, but he should not be able to work into our box."
Liverpool, featuring a debut for new Dutch forward Cody Gakpo, had created little going forward before they fell behind on 26 minutes.
In a catalogue of errors, Thiago first lost the ball from an Alisson throw out and when the ball then came back to the Liverpool goalkeeper he passed it straight to Guedes who gratefully accepted with a simple finish.
The hosts, seemingly a little shell-shocked from the concession, offered little to suggest an equaliser was forthcoming. But a moment of brilliance saw them go into the half-time interval on level terms.
After a giveaway in midfield, Trent Alexander-Arnold picked the ball up on halfway and nailed a spectacular diagonal pass onto the foot of Nunez who expertly side-footed home first time on the volley.
Having coming out of half-time with more intensity, Liverpool soon found themselves in front.
There was an element of fortune involved as Salah was clearly in an offside position from a pass over the Wolves defense. But Toti's attempted headed clearance fell to Salah's feet and was deemed by a VAR review to render the Egyptian onside before he turned and finished into the corner of the net.
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That seemed like it would be that for Wolves' challenge but more hapless Liverpool defending allowed them to tie the game up once more at 2-2.
Hwang was allowed to surge toward the Liverpool box before slipping the ball to fellow substitute Matheus Cunha and sliding in to meet the return pass with his effort deflecting off Ibrahima Konate and back against the forward before squirming through the legs of Alisson.
More drama was to come when Wolves thought they had a stunning late winner through Toti only to be denied by the raising off an offside flag. A long VAR check followed but, to the anger of Wolves boss Julen Lopetegui on the sideline, offside was confirmed.
While Wolves were left feeling they could have had more, they will have another chance to knock out last season's FA Cup winners in a home replay in around 10 days' time.
Information from Reuters contributed to this report.