Neighbours, who grew up in nearby Airdrie, Alberta, had family and friends on hand.
"(It's the) first time I scored here in the NHL, so it was pretty special," Neighbours said. "And just special having my family and friends here and being able to perform for them, get a win in front of them is really nice."
Thomas scored on the power play at 14:25 to give the Blues a 2-1 lead. He took a pass from Jimmy Snuggerud and wristed a shot over Wolf's left shoulder.
Coronato scored his second of the game 32 seconds later to tie it 2-2. He took a long pass from Kevin Bahl and scored with a wrist shot from the right circle.
"There's obviously going to be momentum swings in games too with power plays, penalty kill," Flames defenseman Rasmus Andersson said. "They have a good shift, we have a good shift, but I thought overall the first two periods were good by us."
Neighbours tipped in a shot by Colton Parayko at 11:07 of the third period to give the Blues a 3-2 lead.
"He was really tenacious," Montgomery said of Neighbours. "He's had a really good friend pass away (recently), so it was an emotional moment for him, not just because it's his hometown, but he's been dealing with a little bit of loss and that's not easy. He's a tremendous character kid, someone that I'm sure will wear a letter [for the Blues] one day."