Cullen was beaten 4-3 in a sudden-death decider in one of the finest matches ever seen on the Alexandra Palace stage.
The 16th seed twice had a shot at bull to win the tie and reach the quarter-finals, but Van Gerwen held his nerve to snatch the deciding leg and remain on course for a fourth title.
The Bradford ace fired in an astonishing 19 maximum scores of 180, equalling the tournament record for a seven-set match.
Cullen went 1-0 ahead despite missing nine set darts and had an opportunity to double his lead, but failed to land double nine.
He held his throw to go 2-1 up and then moved to within one set of the match by breaking top seed Van Gerwen in the next.
The Dutchman won the next set, but Cullen sent the seventh into a deciding leg and missed a shot at the bull to win the match.
Van Gerwen levelled the scores at 3-3, but Cullen had the advantage of the throw in the final set and was again narrowly off target with a shot at the centre of the board to win the tie in the fourth leg.
Van Gerwen rode his luck to square the set at 2-2 and then opened the deciding leg with a maximum, ensuring Cullen wasn’t given another chance.
Yorkshire-based South African Devon Petersen will play two-time former champion Gary Anderson in the last 16 of the PDC World Darts Championship.
Petersen, who lives in Bradford, swept to a 4-0 whitewash of Jason Lowe.
The ‘African Warrior’ hit nine 180s and dropped only five legs in a dominant third round performance.