Making his first quarter-final at a major, De Decker averaged just shy of 96 to end the hopes of Scotland's Anderson.
The Belgian raced into the lead by whitewashing the opening set before taking the second with a 120 finish, then holding throw in the third to seal the match.
"It's massive," De Decker told Sky Sports. "I always had a problem bringing my floor game to the stage but it's clicking this week and I hope I can keep this up.
"I'm just trying my best every single game. I'm not keen on all the attention and I'm just doing my thing."
De Decker's quarter-final opponent will be James Wade, who dominated his match against Wales' Gerwyn Price to win 3-0.
Wade edged a tight first set before taking the second comfortably and closing out the match in a nervy ending.
Thursday's other results saw Joe Cullen win an entertaining encounter against Northern Ireland's Daryl Gurney 3-2 and Dimitri Van den Bergh beat Dave Chisnall 3-1.