Wesley Verhoek curled the ball round Ajax and Netherlands goalkeeper Maarten Stekelenburg on the stroke of half-time to seal Den Haag's first win away to Ajax in 24 years.
For Ajax it is the third time this season they have dropped points after a midweek Champions League match, the defeat leaving them on 27 points from 13 games, four points adrift of Twente who have PSV a single point behind.
Balazs Dzsudzsak netted a rebound after 25 minutes to put the Eindhoven club ahead but seven minutes later they were reduced to 10 men after a red card for striker Jonathan Reis.
Utrecht's Jacob Lensky also was sent off, conceding a penalty that Dzsudzsak converted, before Frank Demouge pulled one back.
Twente beat Excelsior Rotterdam 2-1 on Saturday.
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