The Reds stuck with the same starting line-up that did the business over Manchester United in Sunday’s 2-0 victory at Anfield, with Wolves doing likewise.
In no less than eight minutes, Jordan Henderson exploited an open gap in defence from a corner to head in from the near post from Trent Alexander-Arnold's out-swinging corner.
Wolves could have drawn level three minutes later when Ruben Neves swung in a cross from the left, but Matt Doherty headed across the far post with the defence caught square.
Mohamed Salah looked to give Liverpool a second on 17 minutes, but saw his shot blocked away by Doherty from the intended target after a darting run into the area.
An injury casualty shortly from the half-hour mark signalled the end for Sadio Mane, who picked up a knock and was replaced by Takumi Minamino for his league debut.
However, Wolves were level five minutes after halftime when Raul Jimenez leaped to a cross from the right to find the bottom far corner.
Jimenez was in for his brace as he beat the offside trap to go level with Alisson Becker on 68 minutes, but the effort flew right at the Brazilian from close-range.
Roberto Firmino sealed the all the points on offer in the last eight minutes after beating two bodies in the area to lash home Henderson’s through ball.
Wolves missed a big chance for a point late on as a cut back in the area from Jimenez found Diogo Jota who fired over the top, with Liverpool holding on to claim a 14th consecutive league victory.