PSV Eindhoven are still looking for their first win of the season after sharing the points with Twente Enschede in a 1-1 draw in the Dutch league on Sunday.
Twente pushed aside memories of Tuesday's last-minute Champions League elimination by Portugal's Sporting in the third qualifying round by opening the scoring in the 19th minute through Brazilian Douglas.
Six minutes later Balazs Dzsudzsak replied for the visitors.
After two matches, only Ajax Amsterdam and Utrecht have scored the maximum six points. Twente have four, while PSV who also drew their opening match, have two.
Champions AZ Alkmaar, 2-0 winners over Sparta Rotterdam on Friday, have three points.
Japanese international Keisuke Honda struck twice on Sunday to earn newcomers VVV-Venlo a 2-2 home draw against ADO Den Haag, who had taken an early two-goal lead but ended with nine men after red cards for Karim Soltani and Ricky van den Bergh.
In the day's other matches, Utrecht beat Willem II Tilburg 1-0, while there were goalless draws in the games between NAC Breda and Heracles Almelo and Vitesse Arnhem and Feyenoord.
Suarez hits hat-trick as Ajax cruise past Waalwijk
Uruguayan striker Luis Suarez scored a second-half hat-trick for Ajax Amsterdam in a 4-1 home win over RKC Waalwijk on Saturday to make it successive wins under new coach Martin Jol.
Gregory van der Wiel opened the scoring for Ajax after 10 minutes but Benjamin de Ceulaer fired Waalwijk, who Jol managed between 1998 and 2004, level 14 minutes before the break.
Waalwijk were reduced to 10 men for the final 19 minutes after Wouter Gudde received his second booking for a foul on Suarez, who converted the penalty.
A powerful long drive from the Uruguayan put Ajax, who opened their season with victory at Groningen last weekend, 3-1 up and he completed his hat-trick in injury time from close range.