PSV Eindhoven, 5-1 winners at Heracles Almelo on Saturday, are top of the standings with 43 points after 20 matches, one ahead of Twente Enschede who were held to a 0-0 draw by Feyenoord.
Ajax grabbed the lead 12 minutes before the interval when Guram Kashia deflected a shot from Lasse Schone for an own goal. Christian Eriksen doubled the lead after 64 minutes with a header.
Theo Janssen pulled one back four minutes later for Vitesse after hesitant defensive work from Joel Veltman before Patrick van Aanholt and Renato Ibarra both came in from the flanks to turn the match around.
"Our defending was too naive and allowed them to fight back in the match and that should not happen on this level," said Ajax manager Frank de Boer.
Vitesse coach Fred Rutten said Janssen's self-belief had inspired the win. "Before that we played without any confidence," he said.
The teams will meet again on Thursday in the quarter-finals of the Dutch Cup.
Ajax remained third with 40 points while Vitesse move to fourth with 38 points on goal difference ahead of Feyenoord.
Steve McClaren's Twente never displayed the will to go for the win which would have put them top of the standing and were lucky to reach the break 0-0 after Lex Immers and Tonny Vilhena wasted good chances for the home side.
Twente regained control in the second half but came no further than a close-range chance for Dusan Tadic who was denied the winner by keeper Erwin Mulder.
In other action sixth-placed Utrecht beat bottom side Willem II Tilburg 3-1 thanks to second-half goals from Anouar Kali, Edouard Duplan and Bob Schepers.