Fiala scored on a spinning backhand two minutes into the extra session to give the Kings their third win in four games.
“That’s a really hard goal to score,” interim coach Jim Hiller said. “He was at the end of the shift already. … I wouldn’t have liked to see that thing go the other way. I know we were tired, we were a little worried about that, but give Kevin credit.”
The Kings remained in third place in the Pacific Division, extending their lead by two points with a game in hand on Vegas, which lost 3-1 at home to Vancouver on Thursday.
Jacob Moverare scored his first career goal, Quinton Byfield and Pierre-Luc Dubois each had a goal, and Cam Talbot made 28 saves for the Kings.
“We needed two points tonight, and I think it showed with our effort,” forward Blake Lizotte said.
Drake Batherson had a goal late in the third period to tie the score 3-3, Dominik Kubalik scored on the power play, and Brady Tkachuk had a goal for the Senators. Joonas Korpisalo, who played for the Kings after last season’s trade deadline, made 31 saves.
“We were right there for the whole game,” said Korpisalo, who returned to the lineup after sitting out three games because of illness. “A couple unfortunate bounces, which decided the result, but I think we played a really good game throughout.”
The Kings came to life in the third, drawing their first penalty and tying it 2-2 with Talbot off for an extra attacker when Dubois finished off Anze Kopitar’s centering pass midway through the period.
Moverare put them in front with 8:14 remaining when his shot redirected in off Tim Stutzle’s stick. It was his first goal in 32 career games.
“It’s gonna be a cool memory to look back to one day,” Moverare said.
Batherson, who also had an assist, sent it to overtime with a one-timer from Artem Zub with 4:23 to go.
Despite being depleted by injuries and having traded forward Vladimir Tarasenko to Florida on Wednesday, the Senators largely outplayed the Kings through two periods.
“I thought we competed hard right from the start,” Ottawa interim coach Jacques Martin said. “We probably could have scored a couple more, we missed some great opportunities. Unfortunately, we only got the one point.”
Kubalik chopped Jake Sanderson’s shot down to go up 1-0 on a power play 7:33 into the first.
After Byfield scored on a breakaway with 6:36 left in the second to tie it, Tkachuk responded 15 seconds later beating Talbot five-hole while falling down to put Ottawa back in the lead.
Talbot made two key saves against Stutzle to keep the Kings in the game, making a pad stop 42 seconds into the first and a sprawling glove save to prevent him from scoring into an open net 13 seconds before Byfield’s goal.
“I think we needed Talbs for the first 40 minutes,” Hiller said. “We didn’t play well. He kept us in it. Not just the obvious with that incredible save he made, but there was five or six before that. He gave us a chance to get our legs underneath us.”
Playing the second night of a back-to-back, the Senators did not have defenseman Thomas Chabot (lower body) and forward Matthew Highmore (upper body), who sustained injuries in a 2-1 loss to the Ducks on Wednesday.
“I think we were just happy the way we played overall tonight,” Batherson said. “For us to come out on a back-to-back and put an effort like that and get a point, we’ll take it.”
Up next for the Kings: vs. the Dallas Stars at Crypto.com Arena on Saturday night.