Belgian forward Divock Origi brought Liverpool, seven-times FA Cup winners, level in the 51st minute with a well-placed effort from the edge of the area.
But Wolves grabbed the winner four minutes later when Ruben Neves struck a superb low drive from 30 yards out.
Liverpool manager Juergen Klopp fielded a much-changed line-up, including two teenage debutants in midfielder Curtis Jones and full-back Rafael Camacho.
The line-up was further weakened in the sixth minute when central defender Dejan Lovren had to go off with a hamstring injury and was replaced by 16-year-old Dutchman Ki-Jana Hoever.
Clearly disappointed with Lovren's injury, especially given he has two other central defenders Joe Gomez and Joel Matip currently sidelined, Klopp said: “I am not sure what you all would have said if immediately from the beginning if our centre-half situation was Fabinho and Ki-Jana; then probably a few very smart people would tell me that I don’t respect the competition or whatever."
Xherdan Shaqiri went close to an equaliser for Liverpool in the 69th minute but his curling free-kick was pushed on to the post superbly by Wolves keeper John Ruddy.
A minute later Klopp brought on Roberto Firmino and Mohamed Salah but Wolves were able to hold firm and maintain their lead.
The reward for Wolves is a fourth round tie against the winner of the replay between Shrewsbury Town and Stoke City.
Wolves's Portuguese manager Nuno Espirito Santo was delighted with the way his team, ninth in the Premier League, had handled Liverpool.
"I am very pleased, the team performed very well in a tough game. We took our chances," he said.
(Reporting by Simon Evans, editing by Pritha Sarkar)
