The Reds were aiming to avoid losing a third successive Premier League away match for the first time since 2012, but fell behind after just five minutes when Hwang Hee-chan’s cross deflected off Joel Matip into the Liverpool net.
It got worse for Jurgen Klopp’s side just seven minutes later as poor defending allowed Craig Dawson to mark his debut with a goal, driving in from close range.
Liverpool managed just one shot on target in a dreadful first-half display, but came out with more fight after the break.
Andy Robertson had a goalbound shot blocked and Mohamed Salah clipped a decent effort just wide of the post, before Darwin Nunez drove straight at Jose Sa as Wolves dropped further back.
But the hosts soaked up the pressure before hitting their opponents on the counter-attack, Ruben Neves finishing after great work by Adama Traore.
Victory moves Wolves out of the relegation zone up to 15th, while Liverpool remain 10th.
Source: BBC