Del Zotto beat Johan Hedberg from the dot in the left circle to give the Rangers (2-0) a sweep of the home and home series with the Devils. Del Zotto also added three power-play assists in the third period.
Henrik Lundqvist, seeing his first action of the preseason, stopped 25 shots for the Rangers.
Ryan Callahan, Matt Gilroy, Artem Anisimov and Ruslan Fedotenko also scored for New York.
Zach Parise set up three goals but it wasn't enough as the Devils fell to 0-3 in the preseason, with every game going to overtime or a shootout.
Ilya Kovalchuk, Andy Greene, Matt Taormina and Brian Rolston scored for the Devils.
Parise set up both first-period goals as the Devils took a 2-1 lead.
Kovalchuk struck first with his second goal in two games. The Devils' $100 million winger took a feed from Parise and picked the shortside on Lundqvist at 2:51.
A wide-open Callahan pulled New York even at 3:33, converting a pass from Fedotenko who eluded Devils defenseman Henrik Tallinder along the boards.
Parise make the key play again, sliding the puck to defenseman Greene who beat Lundqvist from the high slot at 5:58.
In the second, Parise did the dirty work to keep the puck alive behind the Rangers net that led to Taormina's drive from the left point that put New Jersey ahead 3-1 at 13:11.
Gilroy scored on the power play 1:06 into the third as the Rangers trimmed the Devils lead. Although he didn't get an assist, Sean Avery played an instrumental role by screening Hedberg from just outside the crease.
Rolston restored New Jersey's two-goal advantage at 4-2 with his tally at 5:36.
But the Rangers pulled even at 4 on power-play goals by Anisimov at 10:01 and Fedotenko, a blast from the top of the right circle, at 12:33 that sent the game into overtime.