Liverpool moved to the top of the Premier League after goals from Ibrahima Konate's header and a Mohamed Salah penalty either side of Rayan Ait-Nouri's Wolves equaliser made it five wins from six league games.
Defeat at home to Nottingham Forest a fortnight ago remains their only blip as they have also won in the Champions League and Carabao Cup in a promising beginning to Arne Slot's reign.
It is early days, but the evidence suggests they have the capacity to challenge for the title alongside Manchester City and Arsenal.
Wolves' expectations are much lower as their wait for a first win of the season goes on. Circumstances and fixtures have not been kind in the opening six games, but boss Gary O'Neil knows wins will have to come soon.
Their performances have not been as bad as results have suggested and they again settled well, keeping Liverpool at arm's length, even if they had to endure some nervy moments playing out from the back.
They enjoyed a good spell after 20 minutes when several balls went into the box before Matheus Cunha saw a curling effort plucked out of the air by Alisson Becker.
But it was the goalkeeper at the other end that was kept busier as Sam Johnstone produced two important saves.
The first was a routine stop to collect a low Trent Alexander-Arnold free-kick, but the second could be a contender for save of the season.
Liverpool got in down the left in the 40th minute and Andrew Robertson put it on a plate for Dominik Szoboszlai, with an inviting cross that only needed tapping in from five yards out.
However, Johnstone flung himself across goal and somehow kept the ball out with his leg.
But the England international will be disappointed as he was beaten in first-half injury time.
Former Wolves forward Diogo Jota clipped in an inviting cross from the left and Konate rose highest to power a header past Johnstone, who got a good hand to it.
It was a killer time for Wolves to concede and they nearly handed their hosts a second in the opening exchanges of the second half.
Some more risky playing out from the back saw Mario Lemina pass straight to Salah but, with the goal unguarded, he fizzed an effort wide.
And it was some equally generous play from Liverpool's defence at the other end which saw Wolves equalise in the 56th minute.
Konate thought he was shielding an overhit through ball for Alisson to collect, but the goalkeeper did not come for it, with Jorgen Strand Larsen nipping in, and after a scramble Ait-Nouri converted from close range.
It was just the tonic Wolves needed but they were level for less than five minutes.
Two-and-a-half minutes after the equaliser Nelson Semedo hauled down Jota in the penalty area and Salah converted from the spot.
Wolves showed plenty of heart and spirit but they could not forge a better chance to equalise than the one that saw Carlos Forbs' shot brilliantly blocked by Konate as he atoned for his earlier error.
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