Van Duijvenbode started well, but the match was whipped from under him as Anderson won 10 straight legs.
Two-time winner Anderson landed the first of three match darts at double top at Alexandra Palace to close out.
World number one and three-time champion Van Gerwen takes on England’s Dave Chisnall in the evening session.
Chisnall is aiming to make the last four for the first time and inflict Van Gerwen’s first loss at the last-eight stage of the tournament.
Earlier on Friday, England’s Stephen Bunting beat Poland’s Krzysztof Ratajski 5-3 to book his place in the last four.
Bunting will play the winner of Welsh third seed Gerwyn Price’s meeting with Northern Ireland’s Daryl Gurney, which takes place later on Friday.