James Neal had the winner, at 9:24 of overtime, and his shot from the left circle went in off Ducks forward Corey Perry, who was in front of Gibson.
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Another night, another bizarre goal.
"It's been going on all playoffs," Gibson said. "So no different."
The flukes, the odd bounces and goals off teammates would test the patience of even a seasoned veteran. Gibson made an NHL postseason career-high 43 saves and was especially busy through the first 40 minutes. Nashville outshot Anaheim 15-6 after one period, 32-17 after two and 46-29 in the game.
"You can see the shots, they were coming pretty hard there," defenseman Sami Vatanen said. "We didn't have the skating legs maybe going at that time. [Gibson] made huge saves and kept us in the game and after that it opened up. He's been good this year, like all our goalies."
Ducks coach Randy Carlyle said they can't afford to have a slow start in Game 2 on Sunday.
"We were pretty inept in what we were doing and we were receiving the game," Carlyle said. "Our goaltender should get full credit for keeping us in the game."