Thatcher Demko made 23 saves for the Canucks (6-11-2), who have one win in their past seven games (1-5-1).
"It's frustrating that we lost tonight. I'm not disappointed in how we played," Canucks coach Travis Green said. "Probably take that game every night, probably win it eight or nine times out of 10."
Fleury was at his best with Chicago being outshot 30-13 through two periods, including getting enough of Vasily Podkolzin's point-blank redirection that hit the post at 17:30 of the second.
After Tanner Pearson hit the crossbar off the rush at 8:00 of the third, Fleury made six saves during a power play with 2:18 left in regulation and Demko pulled for an extra attacker.
"It's fun when it doesn't go in," Fleury said. "Definitely some help from my posts. I'll buy them dinner, or maybe fresh paint. Just treat them a bit. They were good to me. I think they had like four or five posts. It's fun, though. It's a challenge and if I can keep the game close, I always believe we can get some goals and we did get a huge one there in the third."
Hagel scored by winning a battle with defenseman Tyler Myers in front of the Vancouver net and screening Demko as he tipped Erik Gustafsson's point shot.
It was Hagel's second game back after missing three with a shoulder injury. He also had to leave the game in Edmonton for a stretch because of what he described as "dead arm" after getting hit.
"I think it'll be there for a little bit," Hagel said. "Time will heal but I wanted to get right back in there and at this point it's pain tolerance. I feel good enough to go, so I want to get out there."
After dominating play through two periods, the Canucks only had four shots in the third period before the late power play.
"They probably found their legs in the third," forward Connor Garland said. "… They found their legs and they pushed."
NOTES: Fleury passed Roy Worters (67) for sole possession of 14th place on the NHL shutouts list. … Fleury became the fourth Blackhawks goalie to have a shutout at age 36 or older. The others: Tony Esposito, Hugh Lehman and Nikolai Khabibulin. … Chicago defenseman Riley Stillman left the game at 8:56 of the first period with an apparent left leg injury when Canucks forward Tyler Motte fell into the back of his legs after getting cross-checked from behind. There was no update after the game. … Chicago defenseman Calvin de Haan returned after missing his first game of the season on Saturday with right wrist soreness and blocked one shot in 20:38 of ice time.