Former Wolves winger Diogo Jota stung his former club with the game's only goal just before half-time. From a breakout near midfield, Sadio Mane and Mohamed Salah played a one-two before Mane laid the ball off for an onrushing Jota to squeeze his low shot inside the near post.
The half-time lead marked the first time Jurgen Klopp's side had been ahead at the break in nine Premier League matches dating back to January.
The goal was also Jota's first with the club since Nov. 28, and his first since returning from a knee injury earlier this month.
The game took a scary turn just minutes from full time after a collision between Patricio and defender Conor Coady left the Portugal No. 1 motionless on the pitch. Patricio, who appeared to suffer a head injury in the clash, required 10 minutes of medical attention before being stretchered off the field and replaced by John Ruddy, who came on as a concussion substitute.
"He's conscious, he remembers what happened and is aware," Wolves manager Nuno said of Patricio's status after the match.
The tempered victory moves Liverpool to sixth place with 46 points from 29 matches, five points behind Chelsea for the final Champions league spot and two behind fifth-placed West Ham. Wolves, meanwhile, remain 13th with 35 points.
Jota had no qualms about sinking his old club in Liverpool's bid to climb into the Champions League spots.
"It's a special game," he told the BBC.
"I worked here for over three years. I know almost everyone in that dressing room. I just wish the fans could be here to make it even more special.
"If we play the way we have here I think we have a chance of the top four."