Watson gave the Predators a 1-0 lead at 5:47 of the first period. Subban faked a slap shot above the right face-off circle before taking a wrist shot that was deflected at the top of the crease by Brian Boyle. The puck bounced off Bishop's glove to Watson in the slot.
Comeau tied it 1-1 at 5:20 of the second when he scored with a wrist shot from the top of the left hash marks off a pass from Faksa on a 3-on-1 rush.
Dallas outshot Nashville 14-8 in overtime.
The Predators power play went 0-for-4, the fourth beginning with 1:53 left in the third period and extending into the first seven seconds of overtime. They were 0-for-15 in the series after finishing last in the NHL in power-play percentage during the season (12.9 percent).
"I'm part of the power play, so I take full responsibility for that," Nashville captain Roman Josi said. "It's a huge part, and you saw it in the playoffs. Even tonight we had the chances, and if we got a goal there, it's a different game."
The teams split the first four games, each going 1-1 at home, before the Stars won 5-3 in Game 5 at Nashville on Saturday to force the Predators into a must-win situation.
"There are things I thought we cleaned up from the previous game," Nashville coach Peter Laviolette said when asked to assess the series, "but you'd have to go game by game to break that whole thing down. In the end, they got it done tonight. We didn't."