In a matchup of former teammates, Roberto Luongo got the best of Schneider - who used to be his backup in Vancouver. Luongo turned aside Travis Zajac, Adam Henrique and Patrik Elias in the tiebreaker to make Santorelli's goal stand up.
It was New Jersey's second loss to Vancouver this season, and Schneider, acquired in a draft-day trade over the summer, played in both of them. The Devils are just 1-5-4 overall, and the only things keeping them out of last place in the newly formed Metropolitan Division are the similar slow starts by the New York Rangers and Philadelphia Flyers.
''Not a very good one by me,'' Schneider said. ''Just two real bad goals that cost a point. We should've never went to a shootout. No disrespect to Vancouver, I thought I kind of gave them two goals there. (Luongo) made some big saves in the third, they hung around and won the shootout.
''So, it's my fault we lost the point tonight.''
The Devils took a 1-0 lead just 5:05 into the game when Andrei Loktionov found Elias for a shot from the left circle that resulted in his third goal. Elias had missed the previous two games because of illness.
Ryan Kesler tied it at 6:07 with his fifth goal as the Canucks won for the second time in three nights.
''It was an ugly one, for sure, especially in the first two periods,'' Luongo said. ''But we found a way to get it done.''
New Jersey went back in front with a power-play tally 3:34 later on Eric Gelinas' first NHL goal. Gelinas was called up from Albany of the AHL on Wednesday.
Vancouver tied it at 2 with 7:23 left in the second when Daniel Sedin netted his fourth of the season. Sedin fired a slap shot off a dump-in that found its way under Schneider's right pad.
Luongo made 28 saves before the shootout. Schneider stopped 19.
''It wasn't easy,'' Luongo said. ''I was trying to freeze everything, so guys could get breathers. We dug deep. Everybody had to chip in.''
''I thought we were the better team, obviously for 65 minutes,'' Elias said. ''Unfortunately, you know how we end up after overtime. I think we should put a little more into overtime, but we had plenty of chances to end the hockey game.''
Vancouver coach John Tortorella - back in the New York metropolitan area this week after being fired by the Rangers this summer - was victorious in his return to the Prudential Center, where he and New York lost the 2012 Eastern Conference Finals in Game 6 to New Jersey.
''I'm really happy to not only get the one point, but the second point,'' Tortorella said, while quickly pointing to the entertainment value of this grinder of a game. ''I don't think I would have paid for a minute of that game, but it's nice that we came away with the two points.''
The Devils, a year removed from missing the playoffs, are now winless in five tries vs. the Western Conference.
''We played great, we deserved to win. Those guys worked their butts off and played mistake-free hockey,'' Schneider said. ''I made two mistakes and they both end up in the back of the net. It's unacceptable on my part. So, I know I'm better than that, I have to be better than that, and I'll be better (next time). It starts with everyone pulling their weight, and tonight, I was probably the one guy who didn't carry his load.
''It cost the team a point.''
NOTES: Canucks center Henrik Sedin, who had two assists, played in his 641st consecutive game since March 21, 2004, the sixth longest streak in NHL history. St. Louis Blues D Jay Bouwmeester is the only active NHL player to appear in more games, dressing for 642. ... Elias' goal was his 11th against Luongo in 20 games. ... Devils defenseman Bryce Salvador missed his second game and was designated as a non-roster player due to a death in the family. ... Gelinas played in his second NHL game. He made his debut last season on April 25 against Pittsburgh. ... Vancouver forwards Dale Weise and David Booth left the win with injuries. The Canucks also played without Jannik Hansen, leaving them with just nine forwards.