Yakov Trenin scored twice, and Saros made 34 saves for Nashville, the No. 4 seed, which had won the previous two games each in double overtime.
"I thought it was a hard-fought battle," Predators coach John Hynes said. "Unfortunately, tonight we didn't come out on the right end of the stick. But [I'm] proud of the way we played. We're in a series, so it's on to Game 6."
Teams that win Game 5 after a 2-2 tie are 213-58 (78.5 percent) winning a best-of-7 Stanley Cup Playoff series. Game 6 is at Nashville on Thursday (9:30 p.m. ET; NBCSN, SN360, TVAS, BSSO).
Trenin gave the Predators a 1-0 lead at 11:44 of the first period. After Jani Hakanpää couldn't clear the Hurricanes zone, Roman Josi took a slap shot from the left point that hit Carolina forward Steven Lorentz before fluttering in off Trenin.
"It's such a tight series," Josi said. "There's a lot of chances on both sides, and they just found a way to score in OT tonight. It's a tough loss for us, but we're still in the series and we have to go home and win one."
Necas tied it 1-1 at 14:21 with a wrist shot from the top of the right circle on the power play.
Trenin scored 53 seconds of the second period to make it 2-1, finishing a saucer pass from Colton Sissons on a 2-on-1. Sissons started the play when he gathered an errant drop pass by Pesce in the Predators zone.