The three-time winner cruised into a 9-5 lead before being pegged back to 9-8 as Englishman Cullen hit back.
Dutchman Van Gerwen quickly recovered and won the next two legs to book a quarter-final with Andrew Gilding.
The Englishman comfortably beat Poland’s Krzysztof Ratajski 11-5 in their last 16 meeting.
Ratajski remained in touching distance until Gilding won the final four legs to progress into the next round.
England’s Cross sealed his place in the next round with a convincing 11-6 win over compatriot Ryan Searle.
Cross looked at his fluent best as he finished with an average of nearly 107 to move into the quarter-finals.