Mohamed Salah gave Liverpool the lead in the first half after Wolves defender Conor Coady misjudged a long ball from Jordan Henderson.
Georginio Wijnaldum added a second after the break, bending a superb shot into the top-right corner from long range, before Joel Matip's thumping header and Nelson Semedo's scrambled own goal made it 4-0.
Wolves were largely contained by the home side but had a glimpse of hope when referee Craig Pawson awarded a penalty to Wolves in the first half when he adjudged Sadio Mane to have fouled Liverpool-born Coady.
However he overturned it after reviewing the incident on the video assistant referee monitor, where it was clear there had been no contact.
The win means Liverpool remain level on points with league leaders Tottenham, who beat Arsenal 2-0 in the north London derby earlier on Sunday.
Wolves are in 10th although only two points behind fifth-placed Manchester United, who have a game in hand.
Liverpool fans returned to Anfield for the first time in nine months to see their team who were crowned Premier League champions during that period.
They chanted "bring on the champions" minutes before kick-off and raised their scarves for a spine-tingling chorus of 'You'll Never Walk Alone'.
And the beaming smile on Jurgen Klopp's face as he watched supporters take their seats during the warm-up was still in place hours later after his side produced an entertaining and authoritative performance that kept them in touch with the table-toppers.
Left-back Andy Robertson was a menace throughout for Wolves defender Semedo and he looked the most likely to engineer an opening in the first 20 minutes and it was his fizzed cross that Mane headed just over as the home side pressed for a breakthrough.
However it was skipper Henderson's searching ball that Coady chested into the path of Salah that allowed the Egypt forward to take one touch before firing past goalkeeper Rui Patricio.
The goal was celebrated by those able to snare a ticket for the Kop and they were entertained regularly during the first half, with Roberto Firmino's nutmeg and Mane's Cruyff turn a few highlights.
Liverpool grew dominant after the break when Wijnaldum's wonderful strike provided a two-goal cushion but the biggest roar came when centre-back Matip's header rippled the net in front of the fans.
Trent Alexander-Arnold returned from injury as a substitute to set-up the fourth, Wolves defender Semedo bundling the ball into his own net with Mane poised to score.
Those 2,000 supporters who were denied a victory parade when Liverpool lifted the long-awaited Premier League trophy in July were treated to a performance worthy of champions against a Wolves side who have proved an awkward opponent in recent encounters.
They thanked Klopp's men for a fine performance with another rendition of 'You'll Never Walk Alone' in the final seconds of stoppage time before cheering the manager's familiar fist pumps at full time.