Feyenoord had a golden opportunity to take an even bigger lead over rivals Ajax and NEC, who both dropped points earlier in the weekend, with a win giving Robin van Persie's team a 7-point lead over third-placed Ajax.
The first chance was for FC Twente's Sam Lammers, but it were Feyenoord who really threatened to open the scoring via Anis Hadj Moussa, who hit the post early.
Despite the early opportunity, Feyenoord dropped back and let FC Twente dictate the pace of the game. Daan Rots and Sondre Orjasaeter further tested Timon Wellenreuther, but could not beat the German stopper yet.
Van Persie was forced to two early changes due to injuries - Bart Nieuwkoop replaced Gijs Smal in the 32nd minute, but was taken off himself seven minutes later after a collision with Orjaesetter, bringing on Jordan Lotomba.
Polish midfielder Jakub Moder nearly opened the scoring for Feyenoord in the 41st minute, but it was Kristian Hlynsson who broke the deadlock in the first minute of added time with some help from Wellenreuther, who misjudged a shot from the Icelandic midfielder and saw it bounce off him and into the goal.
With only Jordan Lotomba firing a shot at Lars Unnerstall in the first fifteen minutes of the second half, Van Persie shook things with three changes, including Raheem Sterling.
The additions didn't bring the desired swing of play and Twente even doubled their lead in the 71st minute through Orjasaeter, who outplayed Mats Deijl and fired the ball in the top corner for the 2-0 and his first Eredivisie goal.
Feyenoord created just the one chance in the second half and had to make do with a 2-0 loss in Enschede, meaning the Rotterdam giants did not take advantage of Ajax and NEC's missteps earlier in the weekend.
Meanwhile, Twente temporarily leaped over AZ in the table and near NEC and Ajax to just two and three points in fifth place.