FC Utrecht started the match strongly and former Arsenal youth Nacer Barazite missed the target after 13 minutes.
Sebastian Haller then shot wide of the left post from a Utrecht counter-attack.
Andersen nearly doubled the lead before half time but his shot was saved by Robbin Ruiter.
Things got worse for Utrecht in the 41st minute when striker Sebastien Haller was sent off for violent conduct.
That did not stop them getting back into the match though, and the score was level just after the break. Barazite beat the offside trap to pick up Willem Janssen's through ball and fire it into the bottom-right corner.
Willem had regained the lead just five minutes later though when Louis Nganioni turned the ball into his own net.
The points were secured in the 69th minute when Robbie Haemhouts found the bottom-right corner from 10 yards.