The Netherlands’ three-time winner Van Gerwen saw off his compatriot Van Duijvenbode 4-1 at Alexandra Palace, averaging 100.42.
Assessing his performance, Van Gerwen told a press conference: “Average, it wasn’t perfect, but I did some really important shots when I had to.
“I knew Dirk wasn’t playing well and he was trying to find the rhythm, trying to slow me down, speed up, and he didn’t do himself any favours.
“Then you need to say to yourself ‘take a step back, relax a bit and try to punish him’, and that’s exactly what I did. Of course it wasn’t magical, but I won.”
Van Gerwen’s opponent in the last eight will be first-time quarter-finalist Chris Dobey, who defeated 2018 champion Cross as he came from 2-1 down to triumph 4-2.
Last year’s runner-up Michael Smith advanced with a 4-1 win against Joe Cullen and will now face Stephen Bunting, a 4-1 victor over Luke Humphries.
Germany’s Gabriel Clemens set up a last-eight clash with 2021 title-winner Gerwyn Price as he got past Alan Soutar 4-1.
And Dimitri van den Bergh emerged with a 4-0 win from an all-Belgian contest against Kim Huybrechts and will play Jonny Clayton in the other quarter-final.