The capital club retained their four-point gap at the top of the standings thanks to a quickfire double after half-time. Kolbeinn Sigthorsson struck first on 47 minutes before a Tim Gilissen own goal soon after left Ajax on the brink of a 32nd top-flight crown.
Frank de Boer's side will retain their title if they beat bottom-placed Willem II at the Amsterdam ArenA next Sunday.
PSV Eindhoven now appear only to be playing for second place, and Champions League qualification, but took an important step to pinning down that spot after routing FC Groningen 5-2.
PSV scored all their goals in the first half, with Tim Matavz, Dries Mertens and Jeremain Lens on target inside the first 13 minutes. Mark van Bommel got in on the act on 41 minutes before Lens' second arrived on the stroke of half-time.
Groningen earned some consolation after the break through a Michael De Leeuw double.
PSV's win moves them three points clear of Feyenoord, who host Heracles on Sunday.
Roda JC grabbed a crucial win in their fight against the drop as they beat RKC Waalwijk, who occupy the final safety position, 3-1.
Jeroen Zoet gifted Roda a 50th-minute opener and after Sanharib Malki doubled the advantage the hosts were out of sight when Guy Ramos scored a second own goal.
Nourdin Boukhari grabbed RKC's goal on 89 minutes but defeat allowed Roda to move a point behind them.
VVV-Venlo cannot secure automatic safety after they drew 1-1 at ADO Den Haag.
VVV had led for the majority of the contest through Uche Nwofor (14) only for Mike van Duinen to deliver a killer blow six minutes from the end.
VVV's only hope of survival is now through the relegation play-offs, while bottom-placed Willem II are four points behind and still able to catch them.