Tom Ince fired the hosts into a deserved 35th minute lead when the winger collected Andre Wisdom's fine pass and dispatched an effort into the back of the net.
 
Liverpool made sure of their passage into the next round thanks to Krisztian Adorjan netting a Kop end goal in the opening exchanges of the second half.
 
The Reds kicked-off hoping to secure a victory on the first step of their quest to reach a fourth FA Youth Cup final in five years.
 
Last season's final heartbreak to Arsenal had only served to increase the Academy youngsters' desire to reclaim the trophy for a fourth time in the club's history.
 
Wolves had proven difficult opponents just over two weeks previous when they beat Rodolfo Borrell's men with a last-gasp goal in a league meeting in the Midlands.
 
However, Liverpool made an encouraging start to a bitterly cold evening inside Anfield, and Ince could have given the home side a third-minute lead when he burst into the box, only to drag his shot wide of the far post.
 
It was certainly a feisty opening to proceedings, with both teams snapping into challenges on the immaculate surface.
 
With Kop luminaries such as Kenny Dalglish and Jamie Carragher watching on from the directors' box, the young Reds had every reason to want to make an impression.
 
Back came Wolves, and Wisdom had to be alert to block James Spray's dangerous low cross into the six-yard box.
 
Play was zipping crisply from one end to the other in what was proving to be an absorbing encounter.
 
Adorjan stung the palms of visiting goalkeeper Daniel East before Nathaniel Mendez-Laing skipped beyond Jack Robinson at the other end and teed up Spray, who saw his shot on the turn tipped behind by Deale Chamberlain at full-stretch.
 
Such has been Mendez-Laing's progression at youth level, the forward has already appeared for Wolves' senior side this season and was named man-of-the-match for his performance in a Carling Cup tie with Swindon.
 
Liverpool should have broken the deadlock in the 22nd minute. Chris Buchtmann's pin-point ball over the top released Ince through on goal, but the winger delayed his shot prior to skewing wide of the far post.
 
Then, John Flanagan was sent bearing down on East's goal by an imaginative back-heel from Michael Ngoo, but the Reds defender was thwarted by the Wolves custodian. Conor Coady headed over the resulting corner.
 
However, East could do little as Ince finally found the back of the net in the 35th minute.
 
Wisdom's defence-splitting pass sent the Reds No.11 through on goal, and this time he made no mistake with a coolly-taken left foot finish across the 'keeper and into the bottom corner.
 
Liverpool had begun to assume control of the game, and within 60 seconds of the start of the second half, had two opportunities to extend their lead.
 
First, Ngoo scooped wide when well positioned before Adorjan struck into the Kop from the edge of the area.
 
A deserved second did eventually arrive on 56 minutes, though, when the Hungarian forward jinked his way into the box and slotted a low effort beyond an unsighted East from the left hand side of the area.
 
Despite the hosts holding a two goal advantage, the game remained fiercely contested with strong tackles being made all over the park.
 
It was a stern challenge that presented Adorjan with a shooting opportunity from a free-kick on the edge of the area, but he was unable to test East with his 20 yard effort.
 
Wolves should have reduced the arrears when substitute Andre Landell hooked an effort over the bar after being picked out by Mendez-Laing's run and cross.
 
Landell had another chance in the dying moments, but was frustrated by a goalline block by Flanagan.
 
The impressive Robinson could have capped the night in fine fashion for the Reds when a well worked moved carved open a shooting chance for the defender in injury-time, but East did well to repel the strike around the post.
 
Nevertheless, Liverpool had already done enough to deservedly secure a place in the fourth round draw and gain some revenge for the harsh league defeat they had suffered at the hands of Wolves earlier this month.
 
Liverpool Under-18s: Chamberlain, Flanagan, Robinson, Wisdom, McGiveron, Coady, Buchtmann, Roberts, Ngoo, Adorjan (Pepper 84), Ince. Subs: Sama, Jacob, Roddan, Morgan.
 
Wolves Under-18s: East, Metcalf, Reckord, Rooney, Parsonage, Ebanks-Landell, Mendez-Laing, Price, Spray, McAlinden, Ismail (Landell 67). Subs: McCone, Rodgers, Harris, Cranston.
 
Liverpoolfc.tv man-of-the-match: Andre Wisdom