Brian McGrattan also scored for Calgary (12-15-4) while Byron added two assists. The Flames now head out on a five-game Eastern road swing that begins Saturday in Buffalo.
Jeff Skinner scored for Carolina (13-13-7), which is 0-1-2 with one stop to go on a four-game trip. They play in Phoenix on Saturday.
Both goalies played well. Karri Ramo made 29 stops to improve to 5-5-1. Peters, making his fourth start in the last six games for the Hurricanes, had 27 saves to fall to 6-8-2.
Coming on a 30-foot wrist shot that trickled through his pads, it was a soft goal for Ramo to surrender.
Ramo would get a chance to redeem himself less than four minutes later when Smid's hook on Skinner during a breakaway resulted in a penalty shot.
Skinner tried to beat Ramo between the legs again but this time Ramo denied him to keep the game even with 5:25 left in the game.
After an uneventful and scoreless opening 20 minutes, the action picked up in the second. The first notable chance was by Skinner, who beat Ramo but rattled his shot off the goal post.
Later in the second with the game still scoreless, Hurricanes defenceman Justin Faulk pinched in from the blue-line and fired a shot that caromed off both goal posts but stayed out.
Throughout his press conference, Burke alluded to the Flames being too small, not tough enough and needing to play more hostile, or truculent as he likes to describe it.
Appropriately, it was the Flames' most physical player, McGrattan, who opened the scoring at 17:49 the first period.
It was the first goal of the year for McGrattan and his first in 30 games dating back to last season.
Both teams welcomed back veteran forwards to their lineup.
Carolina got Alexander Semin (concussion) back after he missed 12 games.
Notes: The Hurricanes lost rookie Elias Lindholm early in the first period when he was hit hard into the sideboards by Mark Giordano. He will be re-evaluated on Friday. ... Galiardi has gone 21 games without a goal. ... Carolina RW Patrick Dwyer played his 300th NHL game. Calgary C Mikael Backlund played in NHL game No. 200. ... The Flames improve to 7-4-2 with Giordano in the line-up. ... In its last eight home games, Calgary has given up a total of five goals over the first two periods and 14 in the third period and overtime.