Andreas Weimann scored Wolves' second
Liverpool were stunned inside the opening minute as Richard Stearman headed Wolves ahead.
The Championship side then doubled their advantage just before half-time through Andreas Weimann.
Divock Origi got a late consolation for the Reds on 85 minutes but it was too little too late for the home side.
Richard Stearman opened the scoring for Wolves after 60 seconds
Wolves were ahead inside the first 60 seconds thanks to a headed effort from Stearman.
The defender latched onto a deep free-kick from Matt Doherty at the back post to give the Championship side a shock lead.
And Paul Lambert's side soon found themselves 2-0 up just before half-time on 41 minutes thanks to a well-worked team goal.
Wolves broke on Liverpool and Helder Costa poked a through ball to Weimann who cooly rounded Loris Karius before tapping into an open net.
Jurgen Klopp was furious on the sidelines
The second-half saw a small reaction from the home side after Jurgen Klopp threw on Daniel Sturridge, Emre Can and Philippe Coutinho.
Liverpool pulled a goal back on 85 minutes through Origi who smashed in from close range following a header back across goal from Sturridge.
But it was too late and Wolves saw out the four minutes added time to earn a historic 2-1 win at Anfield.
The result means Jurgen Klopp's side have now lost three on the bounce at home and are out of the EFL and FA Cup in the space of a week.