Frank de Boer had warned the reigning champions could ill-afford to slip up against a side that thrashed them 4-0 in the Dutch Cup in December.
However, after PSV's victory against Willem II on Saturday, that is exactly what happened as Serbian striker Durdevic produced a wonderful piece of skill to win the game for Vitesse in the 85th minute.
The striker controlled a high ball into the box on his chest before flicking over a defender's head and turning to power a half-volley into the net from 12 yards for his first Eredivisie goal.
Ajax were therefore condemned to a third defeat of the season, which allowed Feyenoord to close the gap on De Boer's second-placed side to five points with their 2-1 win against ADO Den Haag.
Fred Rutten's men were two goals in front after 20 minutes, Lex Immers scrambling in the opener before Timothy Derijck's clearance ended up in his own net.
Mike van Duinen pulled one back three minutes after half-time but the Rotterdam club held on to remain unbeaten in four.
PEC Zwolle stayed two points behind Feyenoord after a 2-0 success at Utrecht, which came thanks to goals in each half from Thomas Lam and Stef Nijland.
And AZ retained fifth position after Aron Johannsson's early goal set John van den Brom's side on their way to a 3-1 home win against Heracles.
Steven Berghuis added a second after half-time and, although Brahim Darri reduced the deficit, Markus Henriksen restored AZ's two-goal cushion late on.
