The champions were frustrated by sixth from bottom Excelsior until substitutes Mike van der Hoorn and Richairo Zivkovic scored in the last seven minutes.
Ajax had most of the possession but were short on ideas against a resolute home defence.
Van der Hoorn broke the deadlock when he fired in a loose ball and Zivkovic secured the points with his first top flight goal since joining from Groningen in the summer.
Ajax are second with 39 points from 17 matches, four points behind PSV Eindhoven who crushed Go Ahead Eagles 5-0 on Saturday.
Feyenoord are third on 31 points after they won 1-0 at NAC Breda on Sunday.
Colin Kazim-Richards snatched the only goal of the game just after the half-hour mark, his seventh in the league this season.
(Writing by Geert Beckers, editing by Tony Jimenez)
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