Matt Stajan and Lance Bouma also scored their first goals of the season for the Flames (5-3-1), who bounced back from a 2-1 overtime loss they suffered at home to the Tampa Bay Lightning on Tuesday.
Dennis Wideman also scored for the Flames, while Jiri Hudler, Joe Colborne and Kris Russell chipped in with two assists each.
Although the Hurricanes (0-4-2) have yet to win this season, this is the first time they've been blown out. Three of their other losses were by a one-goal margin, while the other two were by two goals, including a 3-1 road loss to the Winnipeg Jets two nights earlier.
Playing in just his third game of the season, Carolina goalie Cam Ward finished with 19 saves in a losing cause.
After losing his first two decisions of the year, Hiller has now won three straight games during which time he has stopped 99 of 101 shots he has faced.
The line of Stajan, Byron and Curtis Glencross helped set the stage for Calgary in the first period in which the Flames outshot the Hurricanes 10-4.
Shortly after ringing a shot off the post, Byron saw Glencross charging towards the Carolina net and fired a slap pass his way. Glencross redirected the puck on net, but Ward slid across his crease to make the stop and end the scoring threat.
Ward also turned aside a pair of point shots off the stick of defenceman Kris Russell during a Calgary power play before standing his ground to stop a shot from the slot by forward Brandon Bollig.
At the other end of the ice, Hiller made a great glove grab to deny Carolina forward Jeff Skinner's break-away attempt.
Wideman opened the scoring when he blasted a point shot past Ward, who was screened by Glencross on the play, to give the Flames a 1-0 lead at 18:18 of the first.
Calgary continued that momentum after the break as Stajan one-timed a pass from Byron past Ward just 32 seconds into the second period.
Monahan then put the Flames up 3-0 at 4:14 of the second when he was the recipient of a nice back-door pass from linemate Jiri Hudler for an easy tap-in goal.
Alexander Semin had Carolina's best chance to score in the second with just over eight minutes left in the period, but Hiller made a nice kick save with his left leg to keep the Hurricanes off the board.
Monahan counted his second of the game at 3:23 of the third when he settled a bouncing puck in the slot before backhanding a shot past Ward.
Less than two minutes later, Bouma drove hard to the net and tapped a pass from Josh Jooris into the Carolina net to put Calgary up 5-0.
Notes: The Flames paid tribute to the tragic events in Ottawa and Quebec by having everyone observe a moment of silence before George Canyon sang "O Canada." … Since sitting out Calgary's 5-2 road win over the Edmonton Oilers as a healthy scratch, Wideman has scored four goals and added one assist in seven games. Wideman has scored four goals in his past five games and all of the goals have been the first goal of the game for the Flames. … Hudler's assist on Monahan's goal in the second period was the 300th point of his NHL career in his 534th game. He added another assist on Monahan's second goal.