Bedard, who has 22 points (11 goals, 11 assists) in his past 11 games, had the first hat trick of his career on Oct. 28 against the Ottawa Senators.
Oliver Moore had a goal and an assist, and Arvid Soderblom made 19 saves for the Blackhawks (10-5-4).
Rasmus Andersson had a goal and an assist, and Matt Coronato scored for the Flames (5-13-3), who are 1-4-1 in their past six. Dustin Wolf made 18 saves.
Ryan Donato put the Blackhawks up 1-0 at 15:05 of the first period. Louis Crevier’s shot from the high slot deflected to Donato, and he scored from the right face-off circle.
Bedard made it 2-0 at 15:11 of the second period after Sam Rinzel lifted the puck down the ice into the offensive zone. Bedard chased after the rolling puck and one-handed it between Wolf’s pads while fending off Flames defenseman Yan Kuznetsov.
Coronato cut the deficit to 2-1 on the power play at 19:32, scoring from the left side of the crease after taking a back-door pass along the goal line from Nazem Kadri.
Andersson tied the game at 3:02 of the third period, putting a shot over Soderblom’s glove from the right circle after taking a pass from Mikael Backlund.
Bedard gave Chicago a 3-2 lead at 4:57 when he sent a wrist shot from the right circle far side after receiving a cross-ice pass from Ryan Greene.
Moore scored off a 2-on-1 with Frank Nazar at 13:04 to make it 4-2. Bedard got his hat trick at 19:19, scoring into an empty net for the 5-2 final.
