Robert Thomas had a goal and an assist, and Pius Suter scored for the Blues (1-1-0), who bounced back from a 5-0 loss to the Minnesota Wild in their season opener on Thursday. Joel Hofer made 27 saves.
Matt Coronato scored twice for the Flames (1-2-0). Dustin Wolf made 24 saves.
Coronato gave the Flames a 1-0 lead with a power-play goal at 14:49 of the first period when his shot from the left side of the net deflected off Blues defenseman Tyler Tucker and past Hofer.
Neighbours took a pass from Thomas and backhanded the puck under Wolf’s legs at 12:41 of the second period to tie the game 1-1.
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 to the top corner 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 over Hofer’s glove.
Neighbours tipped in a shot by Colton Parayko at 11:07 of the third period to give the Blues a 3-2 lead.
Suter redirected Tucker’s point shot past Wolf at 13:33 for the 4-2 final.