The ex-Arsenal and Manchester United striker, 35, curled home from 25 yards after 87 minutes, but was dismissed in the 91st for a late challenge.
Matus Bero had put Vitesse ahead before Eric Botteghin's second-half equaliser.
Vitesse finished the game with nine men after Thomas Bruns and Danilho Doekhi were sent off.
Van Persie scored 190 goals in 383 games for Arsenal and Manchester United.
September 30, 2018