Everything appeared to be going to plan as a Roger Johnson own goal, diverting in Charlie Adam's shot, and another magical Luis Suarez strike appeared to have put the Reds in the comfort zone at half-time.
But substitute Steven Fletcher pulled one back within minutes of the second half starting to ratchet up the pressure on the hosts, who were guilty of missing a number of opportunities to make the victory easier than it turned out to be.
Having lost back-to-back matches at Stoke and Tottenham, where they were humiliated 4-0, it was understandable nerves would be shaky.
And with the Reds keen to avoid a third successive defeat, which would have been their worst run since 2003, the pressure to secure a victory - especially with the Merseyside derby and the visit of Manchester United around the corner - was all-important.
What was equally key to Kenny Dalglish's side's fortunes this season was captain Steven Gerrard making his first Barclays Premier League appearance since March having recovered from a groin operation.
Wolves had actually started the brighter, aided by their hosts' penchant for conceding free-kicks outside their own penalty area.
Their best chance fell to Jamie O'Hara when a ill-judged backpass from Martin Kelly, returning to the side in the absence of the injured Daniel Agger, saw the midfielder shoot weakly at Jose Reina.
A couple of Adam corners caused some difficulties for the Wolves defence but not as much as the midfielder's 11th-minute long-range shot.
Stewart Downing's lay-off saw the Scotland midfielder unleash a 25-yard shot which was diverted past Wayne Hennessey by Johnson's diving header.
Andy Carroll, still the subject of intense debate about his place in the side, should have silenced his critics with a free header from Downing's corner but planted the ball straight at the goalkeeper.
In his favour, however, the England international's performance offered plenty apart from a goal.
But it was Suarez who, once again, was providing the major threat up front with the Wolves centre-backs struggling to contain the Uruguay forward.
Johnson was left bewildered when Suarez brought down Reina's kick and turned the defender inside the penalty area only for his cross to be cut out.
Two further half-chances fell to the South American before he finally got he just desserts in the 38th minute with a goal which owed everything to his movement and Jose Enrique's vision.
The Liverpool left-back lifted a ball over the top of the defence and his team-mate timed his run perfectly to collect, turn Christophe Berra inside then out before firing a shot inside the near post.
Just before the break - during which the third biggest cheer of the afternoon greeted news of former Reds striker Fernando Torres' sending-off for Chelsea - Suarez poked another shot just wide of the far post.
But Liverpool's defensive record this season - they have kept only one clean sheet - meant the third goal would be crucial and it fell to Wolves.
Four minutes after coming on for the start of the second half boyhood Reds fan Fletcher smashed home a shot from Stephen Hunt's cut-back after Reina and Martin Skrtel had got in the way of each other trying to clear their lines.
But Wolves almost crumbled in the aftermath as Hennessey produced his most important save of the game to block Suarez's effort at close quarters from Carroll's knockdown.
Carroll headed against a post while Hennessey made yet another vital block to deny Downing, who should have scored after Liverpool broke quickly on the counter-attack.
Wolves recovered their composure and turned the tables with an extended spell of pressure which caused some consternation amid the massed Red ranks and almost saw Berra equalise with a far-post header.
The long-awaited appearance of Gerrard, who made a brief substitute appearance in the Carling Cup in midweek, finally arrived in the 81st minute when the England midfielder replaced Suarez, who had run himself into the ground.
When the ball dropped to the Reds captain 25 yards out he did not need a second invitation to unleash a dipping volley but there was no fairytale Anfield comeback as the ball bounced wide.
There were a few worrying moments before the end but Dalglish's side saw them out to get back on the winning track.