While third-bottom Everton boosted their bid to avoid relegation, their Merseyside rivals Liverpool crashed to a fourth defeat in their last seven games in all competitions, a miserable run featuring only one win.
Jurgen Klopp's side are languishing in 10th place, 10 points adrift of the top four amid their worst season of Klopp's seven-year reign.
It is the first time since 2012 that Liverpool have lost three successive away league games, while they have already conceded more league goals this season than they did in the entirety of last term.
Facing a struggling team who kicked off in the relegation zone, Liverpool immediately crumbled as Joel Matip deflected Hwang Hee-chan's cross into his own net after five minutes.
Wolves debutant Craig Dawson doubled the lead after 12 minutes when the defender smashed in from 10 yards.
With Wolves fans taunting Klopp with chants of "you're getting sacked in the morning", Ruben Neves sealed the rout with a 71st minute finish from Adama Traore's cross.