Wolves looked confident in the early stages and took the game to Liverpool, even if Jean-Ricner Bellegarde snatched at his attempt from a promising opening.
The hosts’ main cause for concern came from Sam Johnstone's errors with his feet, although Mario Lemina dispossessed Alexis Mac Allister after one wayward pass and the defence dealt with a corner he conceded.
Alisson Becker was initially the goalkeeper using his hands more, stretching to meet Nelson Semedo’s cross and catching a curling Matheus Cunha shot.
Even though Liverpool entered their stride as the half-hour mark approached, the home defence continued to stand firm with Luis Diaz seeing his shots blocked before Johnstone held Trent Alexander-Arnold’s attempt from a free-kick.
It looked certain that Liverpool would make the breakthrough when they first caught out Wolves in the 40th minute as Andrew Robertson picked out Dominik Szoboszlai, but Johnstone instinctively denied the midfielder.
However, there was no stopping Ibrahima Konate, who rose above Toti Gomes to meet Diogo Jota’s cross with a header that squirmed through Johnstone’s clutches for the Frenchman’s first-ever Premier League goal.
After the break, Lemina was fortunate that Mohamed Salah couldn’t find the target after gifting the ball to him inside the box, especially as Wolves were already struggling to form any sort of meaningful fightback with the visitors looking comfortable.
Konate took that too far, though, as he tried to guide the ball out but allowed Jorgen Strand Larsen to reach it and set off a string of Liverpool calamities that culminated in Rayan Ait-Nouri getting the hosts back on level terms.
Wolves’ celebrations were muted almost immediately though, as Semedo pulled down Jota to concede a penalty that Salah clinically dispatched.
Konate then got back up to speed to make a vital block and deflect Carlos Forbs’ effort behind shortly before Salah wasted an opportunity to play through Curtis Jones.
Nonetheless, Liverpool held firm to earn their fourth win across all competitions to take top spot in the Premier League table.
In contrast, Wolves’ solitary win this term came in the Carabao Cup and they occupy 20th place.
Flashscore Man of the Match: Ryan Gravenberch (Liverpool)