Ajax, who have 74 points with four games left, can only be caught by reigning champions PSV Eindhoven who triumphed 2-0 at home to Willem II Tilburg.
"We made it unnecessarily difficult for ourselves," Ajax coach Frank de Boer told reporters.
"The first hour was tough, we had a lot of possession and few chances. But after Klaassen scored we could have got four more."
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PSV went down to 10 men against Willem II when Santiago Arias was sent off for a second bookable offence in the 57th minute.
Marco van Ginkel then gave the hosts the lead 11 minutes later before Luuk de Jong's penalty sealed victory.
Wout Weghorst netted twice as Heracles Almelo won 3-1 at relegation-threatened Excelsior to go fourth.
Heracles have 48 points, four behind Feyenoord who visit Twente Enschede on Sunday.
In Saturday's other game, Vitesse Arnhem and ADO Den Haag drew 2-2.
(Reporting by Mark Gleeson; Editing by Tony Jimenez; mark.gleeson@thomsonreuters.com; +27828257807; Reuters Messaging: Reuters Messaging: mark.gleeson.thomsonreuters.com@reuters.net)
