Wolves had won four of their previous six FA Cup ties against Liverpool, including the most recent such meeting at Anfield in round four a couple of years ago, and they can now add another famous win to their collection.
Ruben Neves struck what proved to be the winner 10 minutes into the second half after Divock Origi had temporarily dragged Liverpool back on level terms, cancelling out Raul Jimenez's goal through the Reds' only on-target shot of the evening.
Liverpool, who had to bring on 16-year-old defender Ki-Jana Hoever early on due to Dejan Lovren's injury, joining Rafael Camacho and Curtis Jones in making his senior debut, have now suffered back-to-back defeats following last week's loss at Manchester City.
Joao Moutinho skied a volley over the crossbar and Willy Boly glanced a header wide as Wolves enjoyed the better of the first half, with the Reds - not helped by the early injury blow that saw Lovren hobble off - struggling to get out of first gear.
The all-Premier League tie threatened to burst into life shortly after the half-hour mark when Ryan Bennett slipped in the box to give Xherdan Shaqiri a shot at goal, but the Swiss attacker dragged the ball horribly wide.
Wolves were ahead six minutes later through Jimenez's calm finish following an error from James Milner in midfield.
The most experienced player on the field was caught in possession just inside the Wolves half of the field and Diogo Jota flicked the ball into Jimenez's path.
Milner failed to close the angle, giving Jimenez a clear shot at goal, which he flashed into the bottom corner of Simon Mignolet's net for goal number seven of the season.
Liverpool offered nothing in response in the remainder of a low-quality first half, but Jurgen Klopp decided against turning to one of Mohamed Salah, Roberto Firmino or Sadio Mane from the bench at the interval.
Klopp's faith in Origi paid off early in the second half as the Belgian striker worked the ball onto his left boot and rifled it past John Ruddy to bring Liverpool back on level terms out of nowhere.
Parity was restored for less than five minutes as Neves, urged to shoot whenever he got on the ball by home fans, did exactly that from all of 30 yards with a swerving low shot that had too much venom for Mignolet.
Shaqiri, on the fringes of things for the first three quarters of the match, sent a near-perfect free kick against the inside of the post - possibly with a small touch from Ruddy - as Liverpool tried to hit back for a second time.
That was as close as the visitors got to snatching a replay, however, even with Salah and Firmino introduced for the final 20 minutes, with Wolves seeing through the rest of the match with relative ease to earn their first win in seven home FA Cup ties.
WOLVERHAMPTON WANDERERS (3-5-2): Ruddy; Boly, Coady, Bennett; Vinagre, Neves, Moutinho, Dendoncker, Jonny (Doherty 75'); Jota (Cavaleiro 52'), Jimenez (Costa 83')
LIVERPOOL (4-3-3): Mignolet; Camacho, Fabinho, Lovren (Hoever 6'), Moreno; Milner, Keita, Jones (Salah 70'); Shaqiri, Sturridge (Firmino 70'), Origi