Sean Monahan and Sam Bennett scored for Calgary (20-17-5), which is 2-5-1 in its past eight games, and 0-4-1 at home. David Rittich made 28 saves.
"It's one of those things," Flames captain Mark Giordano said. "We all play for each other in here, obviously, and we've got to find a way to correct this little slide here and these first periods where we're getting down by three goals."
Maatta scored on Chicago's sixth shot after taking a pass from Kane for a 1-0 lead at 4:14 of the first period, and DeBrincat scored on the power play 1:21 later to make it 2-0 at 5:35 when he one-timed a pass from Strome.
Kane's 377th career goal made it 3-0 at 12:44, which tied him with Denis Savard for fourth in Blackhawks history.
"He had an unbelievable career in Chicago," Kane said of Savard. "He was my first coach. He's been a great friend and mentor since the day I got here in Chicago. Unbelievable person, an unbelievable player. I'm sure that number would've been a lot higher had he spent his whole career in Chicago. Humbled and honored to be mentioned in the same sentence as Denis."
Lehner sprawled to make a paddle save against Johnny Gaudreau at 15:21, and saved Andrew Mangiapane's breakaway at 5:04 of the second period.
"He's been awesome for us all year," Kane said. "We'd like to make it a little bit easier on him, but he's made some great saves. He's stepped up big. I think sometimes we take our goalies for granted. He was unbelievable again tonight."
Strome extended the lead to 4-0 at 9:41 when he shot over Rittich's shoulder off the rush during a 4-on-4.