Ajax Amsterdam came from behind to beat Vitesse Arnhem 4-2 for their first win this season but champions FC Twente were held to a 0-0 draw at home by Heerenveen, their second in a row.
PSV top the standings with six points from two games, two ahead of Ajax.
Balazs Dzsudzsak converted a fifth minute penalty to put PSV ahead after Purrell Frankel was sent off for a last-man foul and Toivonen hit his first minutes before the interval to double the lead.
Ajax replied to Vitesse's opening goal, a fine header by Davy Propper, with a fierce free kick from Jan Vertonghen and a Gregory van der Wiel goal on 40 minutes.
Marco van Ginkel levelled the score two minutes before the break but directly after Siem de Jong struck from close range to restore the Ajax lead before Vurnon Anita settled the match with superb volley in the 58th minute.