Pedro Neto’s first goal of the season put Wolves ahead after just three minutes and the visitors impressed, with a handful of chances that could have seen them increase their lead.
But Liverpool showed their quality to equalise through Sadio Mane before the break.
In the second half Wolves spurned several golden opportunities before two late Liverpool strikes sealed the points. Mohamed Salah found the net first before Andy Robertson grabbed the third.
Bruno Lage made two changes to his Wolves team and switched to the 3-5-2 formation.
Jose Sa replaced John Ruddy in goal, while midfielder Leander Dendoncker came in for Hwang Hee-chan.
Luke Cundle was not included in the squad as he is expected to play in the under-23 play-off final on Monday.
Jurgen Klopp made seven changes after naming a weakened team in mid-week against Southampton, and he started with a 4-3-3 formation.
Despite still naming a very strong team, Virgil Van Dijk and Salah were named on the bench.
The noise inside Anfield was deafening leading up to kikc-off but within just three minutes Wolves had silenced them. Ibrahima Konate made a huge mistake when he got under the ball and missed a header from a Sa goal-kick, allowing Raul Jimenez to race towards goal on the right side. His low cross was smashed home by Neto from close range.
Once Liverpool had settled they saw the majority of the possession. Some nice build-up play saw Diogo Jota dance into the box but Rayan Ait-Nouri did well to get a toe to the ball.
Wolves still looked dangerous, too. Neto did well on the right to swing in a cross and Jimenez was close to meeting it.
A huge Liverpool chance then saw Luis Diaz through on goal but his lofted effort was diverted wide.
In a thrilling battle, Liverpool should have scored when Naby Keita had a free shot inside the box, but Conor Coady made a huge block.
Neto was getting a lot of joy in behind Trent Alexander-Arnold and another good Ruben Neves pass released him. His low cross was met by Dendoncker, who fired wide from six yards when he should have scored.
Moments later, Wolves were handed a huge blow when the lively Neto came off injured after 22 minutes. He was replaced by Hwang.
Shortly after the restart Liverpool equalised. A sublime flick around the corner by Thiago Alcantara put Mane through on goal and he made no mistake with his low finish. The forward got the better of Coady and was played onside by Toti Gomes.
The hosts were dominating the ball at this point and opening Wolves’ defence up at will, as they struggled for an out-ball to create any attacks.
At the time when Villa took the lead against Manchester City, Anfield erupted as the news spread to the fans. However, Hwang was then played clean through on goal, but had his effort saved by Alisson at the near post.
Thiago went off injured just before half-time but Liverpool did not make a change, as they played the last couple minutes with 10 men. An enthralling first half then came to an end with the teams level at 1-1, after an adventurous Wolves performance.
As the teams emerged for the second half, James Milner replaced Thiago while Ruddy replaced Sa. The Wolves goalkeeper suffered a knock towards the end of the first half but continued until half-time.
In the opening minutes of the second half Wolves had a big chance for a penalty waved away by referee Anthony Taylor. Gomes was unmarked and was aiming to get on the end of a free-kick, but was shoved to the floor.
Mane found the net shortly after, to send Anfield into raptures, before a very late flag from the linesman ruled him offside. Shortly after the forward was appealing for a penalty under a challenge from Coady, but nothing was given.
An excellent Ruddy save then denied an Alexander-Arnold effort from distance.
Gomes, who was having a brilliant afternoon, made one mistake and Salah was in. But Willy Boly made a world class sliding tackle to stop the chance.
At the time when Villa’s second goal went in, Anfield once again went bonkers. But in a crazy game Hwang almost silenced them with a shot that needed tipping over the bar.
There was another shout for a penalty, too, when Hwang claimed he was pushed as he diverted a diving header wide.
Wolves were pushing for a dramatic winner. Jimenez was in down the right and had a simple job of squaring it to Hwang, but he overplayed the pass.
Then, Wolves were three on one as Jimenez had Dendoncker and Hwang to choose from. He chose the latter and overplayed the pass again, losing another huge chance.
Liverpool took the lead when Salah squeezed home an effort, following Ait-Nouri's block on the line to deny Joel Matip.
Shortly after, Robertson secured the three points when he finished from close range in the last major action of the game.
The scoreline was harsh on Wolves, who gave a good account of themselves, but the 2021/22 season ultimately finished in defeat.
Wolves: Sa (Ruddy, 45), Boly, Coady, Gomes, Jonny, Dendoncker (Trincao, 90), Neves, Moutinho, Ait-Nouri, Jimenez, Neto (Hwang, 22).
Subs not used: Mosquera, Hoever, Marcal, Chiquinho, Podence, Silva.
Liverpool: Alisson, Alexander-Arnold, Konate, Matip, Robertson, Henderson, Thiago (Milner, 45), Keita (Firmino, 70), Jota (Salah, 58), Diaz, Mane.
Subs not used: Kelleher, Van Dijk, Jones, Minamino, Tsimikas, Elliott.