De Zwaan produced a three-dart average of 106.09, hit seven 180s and had 53 per cent on the doubles as he prevailed in a back and forth contest in which Chisnall himself averaged 101.75.
De Zwaan scored heavily throughout the match, with 31 throws of 140 or more, but Chisnall somehow clung to his coat-tails despite regular dips in his performance and a brilliant 161 checkout forced a deciding set.
De Zwaan drew first blood with a break of throw as he took out 76. He doubled his lead to put himself on the verge of victory with a 10-dart leg and from there was able to finish the job.
Two-time world champion Gary Anderson fought back from the brink of elimination to overcome Ryan Searle in his third-round tie.
The Scot, who celebrated his 49th birthday on Sunday, was heading out when he trailed Searle 3-1 but the Englishman, ranked 52 in the world, fell apart late on and Anderson edged through.
Peter Wright and Seigo Asada had to overcome a delay to their match as Monday night's final clash was put back after a power cut interrupted the action at the Alexandra Palace.
The London venue was plunged into darkness as fans waited for the third round encounter. When play resumed, Wright wrapped up the pre-Christmas schedule with a 4-2 success.
Wright made hard work of it, changing his darts in the middle of the match, en route to hitting eight 180s and a 94.5 average.
In Monday's afternoon session, two-time world champion Adrian Lewis fought back from two sets down to beat Darren Webster 4-3.
Dimitri van den Bergh won 4-2 against Luke Woodhouse to move one win away from a second quarter-final appearance in three years, while Luke Humphries beat Nico Kurz 4-2 to ensure his stay in the competition extended beyond Christmas for the second successive year.