The victory marked the 600th in the career of Chicago coach Joel Quenneville.
Emery, who has prospered since replacing regular starter Corey Crawford during the winning streak, made 22 saves to keep the Blackhawks rolling.
"There's nothing better than winning," Quenneville said. "I've been on some great teams and with some great organizations and some great players and coaches. I'm very content and I've got a nice team to work with."
Chicago jumped out of the gate for a 3-0 lead, getting a first-period marker from Steve Montador and scores in the second period from Niklas Hjalmarsson and Patrick Kane.
Marian Hossa's 15th goal of the season provided a 4-1 cushion for the Blackhawks (21-8-4) in the third as they extended their Central Division lead to four points and leapfrogged the idle Minnesota Wild in the overall standings.
Patrick Sharp assisted on Chicago's final goal to extend his point streak to nine games, the longest in the NHL this season.
Olli Jokinen and Curtis Glencross both scored in the third for the Flames (14-15-4), who concluded a woeful four-game road trip with a fourth straight defeat.
"For the first two periods, we weren't very good," Flames coach Brent Sutter said.
"I'm not going to stand here and say we deserved the game. You can't play 40 minutes of hockey like that on the road and think that you're going to have a chance to win the game."