At the other end of the table RKC Waalwijk were relegated after suffering their 27th defeat of the season, losing 4-1 at Heracles Almelo, with Brazilian Everton scoring twice.
With two matches remaining Twente top the standings with 80 points. Second-placed Ajax Amsterdam will be aiming to reduce the gap to one point when they visit Willem II Tilburg on Wednesday.
Twente's Wisgerhof found his own net in eighth minute to put Alkmaar ahead and although Steve McClaren's side dominated the second half they were unable to find an equaliser.
Twente were also unlucky as they were even denied a penalty despite an obvious handball from defender Simon Poulsen while he was trying to block striker Blaise Nkufo's header.
"Everybody on the pitch and in the stadium saw it (the handball) apart from the referee and the linesman," McClaren told Eredivisie Live Television.
"But even with a draw the situation would be the same for us, we now have to win our last two matches. But if we play like the first half we will win nothing."
PSV Eindhoven, who are third with 73 points, will travel to Heerenveen. Alkmaar leapfrogged Feyenoord to move into fourth on 58.
