Elias Lindholm had a goal and an assist for the Flames (19-14-8), who are 3-1-1 in their past five games. Jacob Markstrom allowed three goals on 11 shots before being replaced by Dan Vladar, who made 13 saves.
"Should win," Calgary coach Darryl Sutter said. "Take one penalty, score two power-play goals, and only give up a handful of shots. Should win the game.
"We got to take the point. We didn't skate (on Saturday) because the Harlem Globetrotters were playing in our building. We had to travel. We couldn't skate this morning because it's a 6 o'clock game. We better be thankful that we got a point because a lot of our young players didn't show up. Lack of preparation. You've got to take them by the hand, some of these guys."
Reichel, who was playing in his third game this season and 14th in the NHL, gave Chicago a 1-0 lead at 2:39 of the first period. He put his stick between his legs and scored on his own rebound after redirecting Seth Jones' point shot.
Blackhawks coach Luke Richardson said Reichel may have earned an extended look after being recalled from Rockford of the American Hockey League on Wednesday.
"I think the idea of bringing him up now is probably he earned a spot," Richardson said. "It's not just a flash, you know, coming up for a game or two. I think it's just to give him an extended time to see if he can sustain what he's doing right now. I'm sure he's driven to do that. We haven't really talked about it.
"We got a few days now. We have [Monday] off, and we got a couple days of good practice, and we can show some video and all the good things we've done over the last few games, and he's part of that, so we expect him to be here."