Super-sub Divock Origi scored a dramatic added-time winner to send Liverpool to the top of the Premier League table.
Jurgen Klopp’s team dominated a one-sided game but looked as if they would fail to score for the first time this season.
But just as a resolute and determined Wolves team looked as if they had slugged out their third consecutive goal-less stalemate Origi struck with a goal that could have huge significance in the title race.
When Mo Salah cut the ball back from the bye line, Origi - who had replaced Jordan Henderson - swivelled and fired home from close range.
Liverpool went into the game with 43 goals from their first 14 League games but for once the finishing touch that had seen them fire four goals in each of their previous three games - against Arsenal, Southampton and Everton - looked to have deserted them.
They squandered a string of great chances as they were held to their fifth draw of the season.
The most incredible miss was by Diogo Jota on the hour after a mix-up between Wolves defender Roman Saiss and his goalkeeper Jose Sa who had come charging out of his goal.
It left Jota with a clear run at an open goal but he waited too long to shoot and when he did Connor Coady blocked his effort on the line.
Former Wolves man Jota had also missed with a diving header in the first half when Trent Alexander Arnold was also a culprit, volleying over from close range after a superb pass by Thiago had set him up.
Sadie Mane had a late chance saved by keeper Sa but Origi came to the rescue in the nick of time.
Sa 7; Kilman 6. Viaduct 7, Saiss 7, Ait-Nouri 7, Neves 5, Dendoncker 6, Senedo 6; Tralee 7, Jimenez 6, Hwang 5.
Alisson 6; Alexander-Arnold 8, Matip 7, Van Dijk 6, , Robertson 7; Fabinho 6, Henderson 7, Thiago 7; Salah 7, Jota 6, Mane 6.