Andy Robertson marked his 200th Premier League appearance by putting the Reds ahead for the first time on 85 minutes, before substitute Harvey Elliott's shot deflected off Hugo Bueno for an own goal to seal the victory in stoppage time.
Cody Gakpo brought Liverpool level at the start of the second half when he converted Mohamed Salah's fizzing cross-shot.
The win moves Jurgen Klopp's side one point clear at the top of the table before Saturday's 3pm kick-offs.
Resilient Reds bounce back again
Liverpool again demonstrated their resilience as they recovered from a sluggish first half to win after conceding the first goal for the third time in five Premier League matches this season.
They offered little as an attacking threat in the opening 45 minutes as their midfield got consistently overrun, going into the break behind.
The substitutes made an impact as Liverpool transformed, with Diaz heading just wide from Robertson's volleyed cross a mere 90 seconds after coming on.
The Colombian was then involved in the equaliser as some neat interplay on the edge of the box saw the ball eventually reach Salah, whose drilled cross-shot was tapped home by Gakpo.
Wolves were looking increasingly out on their feet and it was the visitors who looked the most likely to score.
They duly did with five minutes left when Robertson, captain in the absence of the suspended Virgil van Dijk, ran on to Salah's searching pass and side-footed home from six yards.
Elliott wrapped up the win late on but was denied the goal when it was adjudged his shot took enough of a deflection off Bueno to go down as an own goal by the Wolves defender.
Neto stars but Wolves run out of gas
Wolves manager Gary O'Neil will have reasons to be optimistic despite a fourth defeat from five games this season, leaving the Black Country side near the foot of the Premier League
The home side were excellent in the first half, with midfielders Joao Gomes and Mario Lemina snapping at the heels of the Liverpool players and feeding debutant Jeanricner Bellegarde and Neto to launch rapid counter-attacks.
Neto in particular was excellent and set up the opener when he weaved past three Liverpool players and surged into the area, before crossing low for goalscorer Hwang.
Cunha was made to regret that miss as Wolves faded badly in the second half in the face of a resurgent Liverpool, failing to have a shot on target.
Next weekend's trip to fellow early strugglers Luton already looks like a pivotal encounter.