The hosts were poor throughout but forced their way into the game after Stephen Ward had been controversially sent off for two yellow cards.
The numerical advantage allowed Steven Gerrard to powerfully head home an Emiliano Insua cross after the break.
Yossi Benayoun doubled the lead with a deflected effort from close-range to hand the hosts an unconvincing victory.
The hosts came into the match having won just two of their last eight league games and in the unusual position of being mid-table at the mid-way point of the season.
And while fans will not be convinced they have turned the corner after another stuttering display, the cheers around at Anfield at the final whistle will at least offer Benitez some festive cheer.
Wolves were the better side at times and manager Mick McCarthy will surely point to the dismissal of Ward as the turning point.
Referee Andre Marriner showed the defender a second yellow card - but only after being surrounded by Liverpool players for incorrectly cautioning Christophe Berra.
McCarthy had clearly fancied his side's chances of causing an upset by fielding a full-strength team - a very different approach to Wolves' recent outing against Manchester United at Old Trafford.
But the decision to field an attacking 4-4-2 formation allowed Liverpool to take control of the game in the early stages.
The visitors were fortunate Glen Johnson scooped a shot wide after finding space down the right while Fernando Torres, showing no sign of his long-standing groin injury, then tested Marcus Hahnemann after wriggling free in the inside left channel.
Alberto Aquilani, finally making his first Premier League start, looked comfortable in possession but some ill-advised flicks in and around the box tested the patience of an increasingly nervous Anfield crowd.
And Wolves, inspired by their fine recent form in the league, pushed forward and began to create chances of their own.
Nenad Milijas forced Pepe Reina into action from a free-kick before Kevin Doyle put a sharp header wide from only three yards out.
And the hosts' promising start had well and truly faded by the time Kevin Foley failed to control in the box after being left completely unmarked as the tension and frustration around a freezing Anfield increased still further.
But Wolves' hopes were dealt a blow when Ward was sent off early in the second half in chaotic circumstances.
The left-back, already cautioned for a tug on Benayoun, was eventually shown a second yellow card for a foul on Lucas - but not before referee Marriner incorrectly penalised Berra for the offence.
The decision appeared to galvanise the Reds and they soon took the lead when Insua's teasing cross was met in dominant fashion by home captain Gerrard, leaving Hahnemann with no chance.
Any result still seemed possible as gaps appeared all over the field, however, until Benayoun made it 2-0 midway through the second half.
Another fine cross, this time from Fabio Aurelio, found its way to the Israeli and his shot took a cruel deflection off Karl Henry and looped into the net.
From that point on there was no way back for Wolves but McCarthy can take a raft of positives from another impressive display.
Liverpool fans will be thankful of the points but their side are still a shadow of the team that sat top of the Premier League on Boxing Day last season.