Kenneth Perez put Twente ahead before the break but two goals in four minutes for Alkmaar through Mounir El Hamdaoui and a Peter Wisgerhof own goal put the visitors 2-1 in front.
Twente equalised almost straight away when Nkufo set up Costa Rican Bryan Ruiz before the Swiss international got on the scoresheet himself to leave Alkmaar, who host Arsenal in the Champions League on Tuesday, empty handed.
Twente stay top with 26 points from 10 matches, two points ahead of PSV Eindhoven, who beat visitors Heerenveen 1-0 with Danko Lazovic netting a rebound nine minutes from time.
Ajax Amsterdam remain third with 23 points following a comfortable 4-0 home win over 10-men Willem II Tilburg.
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