Alkmaar have 53 points from 26 matches, one ahead of Ajax.
Den Haag were reduced to 10 men after 25 minutes when Ali Boussaboun was sent off and Ajax substitute Jody Lukoki broke the deadlock just after the break following a superb cross from Theo Janssen.
On the hour, skipper Jan Vertonghen broke through on the left flank and finished with style to seal a sixth straight win for the champions.
PSV Eindhoven climbed to third in the table with 51 points following a 5-1 thrashing of Heerenveen ahead of Twente Enschede who lost 2-0 at home to Feyenoord.
Ola Toivonen put PSV ahead after five minutes only for Heerenveen to equalise early in the second half through an own goal from Erik Pieters.
However, Dries Mertens struck twice, with a curved drive and superb lob, to seal PSV's first win under coach Philip Cocu. Orlando Engelaar and Memphis Depay also were on target.
Feyenoord dominated against Twente and grabbed the lead four minutes after the interval when Nils Roseler headed the ball into his own goal. Sekou Cisse scored the second just before the final whistle.
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