The annual season-opener featured a host of new players for both teams as well as coaches after the departure of Erik ten Hag from Eredivisie champions Ajax to Manchester United and Roger Schmidt from cup winners PSV to Benfica.
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Til, signed from Feyenoord, headed home two first half goals and added a third in the 69th minute as PSV upset the champions at the Johan Cruyff Arena.
Ajax, with Alfred Schreuder as their new coach in their first game since Ten Hag's departure, had taken a 15th minute lead through their new signing Steven Bergwijn, who joined from Tottenham Hotspur, but were 2-1 down at the break.
A cracking left footed shot from Mohamed Kudus pulled the score back to 4-3 in the 72nd minute but Ajax were then reduced to 10 men when substitute Calvin Bassey, another new player, was sent off in the 78th minute.
PSV finished off the goal feast with a stoppage time effort from the 19-year-old Xavi Simons, signed from Paris St Germain.
The new Dutch league starts next weekend.