Otman Bakkal opened the scoring for Feyenoord nine minutes before the interval after excellent work from Ruben Schaken.
On the hour, Rasmus Elm curled a free-kick over the wall to equalise and midway through the second half Kelvin Leerdam was sent off with a straight red card.
Feyenoord's Schaken missed the best opportunity to restore the lead before Holman settled the match.
After seven matches, Alkmaar are top with 18 points, two more then Twente Enschede who drew 1-1 at third-placed Ajax Amsterdam on Saturday.
PSV Eindhoven, 7-1 winners over Roda JC Kerkrade on Saturday, are fourth with 14 points, ahead of Feyenoord on goal difference.
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