Former England midfielder Anderton, snapped up on a free transfer from Birmingham City, had a hand in the opening two goals for Kenny Miller and Colin Cameron.
He then added Wolves' third when Chester goalkeeper Chris Mackenzie fumbled his 72nd minute free-kick.
Scottish international midfielder Cameron grabbed his second in the 74th minute before Vio Ganea marked his comeback from a year on the sidelines with a knee injury by completing what turned into a rout with Wolves' fifth five minutes later.
The final scoreline was tough on a battling Chester side managed by former Wolves skipper Keith Curle.
They had battled well after Miller's sixth minute strike before a flurry of four goals in the space of 17 second-half minutes ended their resistance.
They deserved some consolation for their efforts and they were rewarded seven minutes from time when Ben Davies curled home a coolly taken free-kick from 25 yards following a foul by Wolves' Hungarian international central defender Gabor Gyepes.
Miller gave Wolves the perfect start when he struck from close range - firing home a mis-hit cross from Anderton.
Chester's chances to equalise were few and far between with former Wolves striker Michael Branch denied a goalscoring return to Molineux by a last-ditch challenge from Joleon Lescott after a neat throughball by Stewart Drummond.
Miller, Mark Kennedy and Ki-Hyeon Seol then missed good chances before the floodgates opened in the 62nd minute when Cameron drove home a cross from George Ndah who had been released by Anderton.
Mackenzie then gifted Anderton Wolves' their third ten minutes later before Cameron grabbed his second in the 74th minute after good work by teenage debutant Mark Davies.
Ganea set the seal on the success when Cameron turned provider to allow the Romanian international to lift the ball home at the near post.