Van Persie, who re-signed in January for the club he had left in 2004 to join Arsenal, completed the scoring with an excellent strike from just inside the box in the 78th minute, inside a minute after coming on as a substitute.
Jens Toornstra had put Feyenoord 1-0 up eight minutes into the second half, with Jerry St Juste then doubling the lead in the 72nd minute.
While Jones kept Groningen at bay throughout the contest, one-capped Socceroo Ajdin Hrustic was an used substitute for the visitors.
Eredivise champions Feyenoord move up to fourth place on the table with the win.
Elsewhere, Sheraldo Becker's second-half goal steered ADO Den Haag to a 1-0 home victory over Vitesse.
Becker burst clear and slotted a right-footed effort past Remko Pasveer in the 53rd minute.
The win, the hosts' first in 2018, moved ADO up two places to eighth, three points behind seventh-placed Vitesse, who had been unbeaten since the turn of the year.
