PEC, with 13 points from six games, remained in first position after second-placed PSV Eindhoven (12) were held to a 2-2 draw at Twente Enschede.
Ajax, who have 11 points, had to wait until the 72nd minute for South African international Thulani Serero to open the scoring.
Kolbeinn Sigthorsson quickly helped to make it 2-0 after his effort hit the post and the rebound was turned into his own goal by Maikel van der Werff.
A snap shot by Giovanni Gravenbeek reduced the deficit for PEC on the stroke of fulltime.
PSV twice came from behind against Twente, Memphis Depay ensuring a share of the spoils with a goal seven minutes from time.
Newcomers Cambuur Leeuwarden beat Heracles Almelo 2-0 to claim their second league win of the season while the match between ADO Den Haag and Vitesse Arnhem was called off because of a waterlogged pitch.