Vitesse continued to threaten when Lewis Baker broke away through the middle, but his strike sailed over the crossbar.
Milot Rashica came within inches of putting Vitesse ahead when he latched on to a ball over the top of the Willem defence, but his strike clattered off the post.
The visitors found space in the final third again and Rashica was allowed to raid through on goal, but he was denied by a good save from Lamprou.
In the second half, Willem almost went ahead as Lesley de Sa raided forward and cracked an effort at goal from distance, only to see his strike cannon off the post.
Vitesse got back into the match in the 74th minute when Oliynyk converted a cross at the back post by powering an effort past Lamprou.
However, Oliynyk's game was to end on a sour note when he was given a straight red card in the final minute, although his strike proved enough to earn Vitesse a point.