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.
The result means Jurgen Klopp's side have now lost three on the bounce at Anfield in the space of a week.
They are now out of both the EFL Cup and FA Cup.
More to follow…