Jones stopped 31 shots and came within 3:38 of posting his third straight shutout as the Sharks posted their fourth straight win under former New Jersey coach Pete DeBoer. They also kept the Devils winless at 0-3-1 under new coach John Hynes.
DeBoer, who was fired by the Devils last season, is now 4-0 with San Jose.
Patrick Marleau scored for the Sharks in the opening minute and the goal stood until Adam Henrique tied the game on a power play with 3:38 to play in regulation.
Henrique scored for New Jersey on its first shootout attempt but Jacob Josefson was stopped on the second and Mike Cammalleri missed the net on the third.
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