Twente came close midway through the first half but Hakim Ziyech's free kick flew just over the bar.
Cambuur came back soon after, with Mikhail Rosheuvel missing two chances within three minutes, putting both his strikes wide of the goal.
In the second half, Bruno Uvini had his header saved well before Ziyech was denied for a second time.
Cambuur searched for a late winner through Rosheuvel and Bartholomew Ogbeche but both put their efforts high and wide of the goal.
The result sees Cambuur remain in the relegation places while Twente jump out into 15th place.