The goal came after Fleury made a pad save on Chris Tanev's backhand at 14:07.
"It's like he feels when our team really needs that and he gets activated and gets into it," Blackhawks forward Jonathan Toews said. "I feel like when he starts seeing pucks and we start giving up too many chances he gets better and better. He backs us up when we're not so good in front of him. We don't want to have to rely on him to do that every single night. We have to help him and do things better in front of him. He's getting better and better each game, it seems."
Trevor Lewis (18:39) and Johnny Gaudreau (19:34) each scored into an empty net for the 5-2 final.
"It was probably the toughest stretch of our schedule, playing nine games in 15 days, starting in Calgary, ending in Calgary, so it just felt like one big, long road trip, but I think we did a good job of managing our energy, managing our rest, being fresh in all nine games," Lucic said.
Dube scored on Calgary's first shot, a snapshot past Fleury's glove off the rush 1:19 into the first period for a 1-0 lead.
Hagel scored for the second straight game to tie it 1-1 at 8:57 with a shot from the top of the face-off circle by Markstrom's glove after a Calgary turnover.
"There wasn't much left there, was there," Flames coach Darryl Sutter said. "You could see right at the start. It was one of those games where you're physically there, but not quite sharp mentally."