The two-time world champion was in ruthless form, averaging 87.54 overall and finishing 56 per cent of his doubles in a display that echoed his dominant years.
Cullen, by contrast, endured a torrid evening, averaging just 68.05 and repeatedly faltering on opening doubles, landing just one of his 11 attempts.
Anderson took the first set without reply, closing out on double 10 after a swift 78 checkout, and doubled his lead in the second with three legs on the bounce - including a 14-dart break capped on tops.
Cullen finally showed flickers of life in the third set, but Anderson's experience told as he pinned double 5 to end proceedings.
The win means Anderson advances to face Danny Noppert, who earlier edged past an ailing Stephen Bunting 3-1.
Noppert's steadiness at key moments proved decisive, while Bunting later confirmed he had struggled with a back problem that hindered his scoring and rhythm.
Humphries rattles Ratajski
Elsewhere, Luke Humphries progressed with a 3-1 win over Poland's Krzysztof Ratajski, keeping alive hopes of reaching a third consecutive World Grand Prix final.
Humphries dominated the opening set 3-0, landing a 100 per cent record on his starting doubles and showcasing his trademark efficient scoring.
Ratajski rallied to take the third set 3-1 as Humphries briefly lost range, but the world number one reasserted control with four 180s and two ton-plus checkouts, sealing victory in style with a 104 finish via treble 18, 18, double 16.
Humphries has now won 11 of his last 12 matches in the event and faces Scotland's Cameron Menzies in the next round.
Menzies had earlier upset 2018 world champion Rob Cross 3-1 in an erratic but absorbing contest to open the night.
Despite missing eight match darts, the Menzies finally closed the deal on double 4, having averaged over 98.02 in the second set and landing six 180s to his opponent's one.
Thursday night sees the final round of 16 clashes, with Dirk van Duijvenbode facing Daryl Gurney, Jonny Clayton taking on Luke Woodhouse, Luke Littler up against defending champion Mike De Decker and Gerwyn Price battling Josh Rock.