Chisnall raced into a 2-0 lead against the defending champion, who fought back to level at 2-2 after checking out 127 in the fifth leg of set four.
However, Chizzy regained the upper hand by breaking the Dutchman in the opening leg of the decider.
He won the following leg by taking out 86 and, after Van Gerwen had held throw, he sealed his place in the last four by hitting double 10.
"I'm over the moon, I can't believe it," Chisnall told Sky Sports News.
"He didn't play his best, but I played quite good. This is my best win because it got me into the semi-finals. I put my A game in."