Twente kept the pressure on leaders Ajax after substitute Nacer Chadli grabbed a late winner at Excelsior Rotterdam on Saturday.
Steve McClaren's men knew they needed to win to keep their title hopes alive and now sit four points behind the defending champions, who play on Sunday.
Elsewhere, Mike Havenaar netted a late equaliser for Vitesse Arnhem to earn a 1-1 draw at Heerenveen - denting their opponents' hopes of Champions League qualification.
A win for the home side could have briefly taken them second in the table but they were unable to build on Filip Djuricic's early goal and were forced to settle for a point.
FC Utrecht ensured their Eredivisie safety with a battling 2-0 victory at RKC Waalwijk.
Alje Schut and Alexander Gerndt both scored within the final quarter of an hour to move Utrecht 14 points clear of third-bottom VVV-Venlo, who have four games remaining.
De Graafschap were condemned to at least a place in the Eredivisie relegation play-offs tonight after losing at home 3-2 to nine-man Heracles Almelo.
The home side had taken the lead through Soufian El Hassnaoui but goals from Samuel Armenteros, Ninos Gouriye and Everton turned the game around.
Lerin Duarte was then sent off for the visitors before Michael de Leeuw halved the deficit and the hosts then had five minutes to try their luck against nine men when Mark Looms saw red.
But Heracles held on and ensured De Graafschap will now finish in the bottom three.