Ebi Smolarek volleyed fourth from bottom Den Haag into a sixth-minute lead.
He is the son of former Poland striker Wlodzimierz Smolarek who died earlier this month of unknown causes at the age of 54.
Glynor Plet equalised for Steve McClaren's Twente with a header in the 62nd minute.
Heerenveen, fifth on 51 points, rebounded from a double defeat against PSV in the league and cup by cruising to a 4-1 home victory over VVV Venlo.
Viktor Elm (2) and Filip Djuricic struck for Heerenveen while Bas Dost, the league's top scorer, grabbed his 23rd goal of the season.
Elsewhere, Roda JC Kerkrade beat Vitesse Arnhem 3-1 with Sanharib Malki scoring his 21st goal of the season.
NAC Breda and NEC Nijmegen also drew 1-1.
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