Sent down the left wing by Miikka Salomaki, Arvidsson shot a backhander that deflected off goaltender Martin Jones and went into the top right corner for his first playoff goal.
Jones made 28 stops for San Jose, while Pekka Rinne saved 15 of 18 shots.
Game 7 is on Thursday in San Jose. The home team have won all six games in the series.
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It was the series' second overtime win for Nashville, who took Game 4 in the third extra period.
San Jose grabbed a 3-2 lead in the third period on the power play when Logan Couture wristed home his sixth goal of the playoffs off a Brent Burns feed at 10:04 as Rinne stumbled in the crease and could not get to it.
Nashville's Colin Wilson tied it at 12:44, stuffing home a James Neal feed at the left goalpost for his fifth goal of the playoffs and forcing the second overtime game of the series.
San Jose quieted the raucous sellout crowd with two goals from Chris Tierney in less than two minutes midway through the first period.
At 9:55, Tierney got his stick on a wrister from the point by Marc-Edouard Vlasic for his second goal of the playoffs. The play survived a short replay review, the officials' ruling that Tierney's stick was below the crossbar clearly correct.
Tierney, who tallied only seven goals in 79 regular-season matches, made it 2-0 at 11:51 by stuffing home the rebound of a Matt Nieto shot on his backhand.
But Nashville got back into the game with Roman Josi's first goal of the postseason at 15:27 on a backhander that took a weird bounce and jumped over Jones. Prior to that goal, Josi had tried 38 shots without scoring, more than any player left in the postseason.
Ryan Johansen tied it during a 4-on-4 sequence at 1:25 of the second with a great backhand move, slipping the puck through Jones' legs for his fourth postseason marker.
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