The visitors looked the more likely in the opening 15 minutes, but it was Willem II that opened the scoring when Jerson Cabral tapped the ball in from close range following a quick counter-attack.
The striker was on target again a few minutes later when Terell Ondaan provided the through-ball, leaving Cabral with a simple finish to double the lead within four minutes.
Twente were back in the match just before the break though after they won a free kick 25 yards out, which Hakim Ziyech lashed in directly from the set piece.
Ziyech was involved again early in the second half as he popped up at the near post to lash a shot past Kostas Lamprou, levelling the scores.
Ondaan immediately had a chance to restore Willem II's advantage, but his ferocious shot from range came back off the crossbar.
Ondaan continued to pose a threat for the hosts, lofting the ball in for Dijk just before the hour mark, but the defender's header was a fraction wide.
The visitors started to push forward again late on as they looked to complete the turnaround, but Castaignos came closest when he attempted to drive it in from the edge of the box, forcing a save.
The result moves FC Twente up to eighth in the table, while Willem II remain 10th. body check tags ::