Flames forward Johnny Gaudreau controlled the puck from behind the net and fed Lindholm in the slot, beating Nedeljkovic and putting the Wings behind on the scoreboard for the first time this season.
The deficit grew to 2-0 just over four minutes later.
Nedeljkovic made the save on a point shot by defenseman Rasmus Andersson from the point, but the puck dribbled into the slot. Mangiapane found the puck in a maze of sticks and backhanded a shot past Nedeljkovic at 14:33, Mangiapane's second goal.
Markstrom kept the Wings off the scoreboard in the period, his best save arguably on Pius Suter, who had a prime opportunity in the slot.
Tkachuk ended any suspense with an empty net goal, just moments after Nedeljkovic raced to the bench, Tkachuk's first goal of the season.
The Wings have talked all homestand about the need to get the season going on a winning note, and not climbing out of a hole in the standings.
"The first 10, 15, or 20 games and get out in front of those and just play good hockey and try to have a winning record," forward Tyler Bertuzzi said early in the week. "Build from there. The chemistry, it's there, and it's going to continue to be there.
"If we can just keep playing the way we are doing, playing a little bit smarter and just doing it the right way, we're going to get some more wins."
Coaches like to break the schedule into segments and Jeff Blashill is no different.
Blashill said Wednesday he likes to break the schedule into five-game intervals, while grading players individually into 10-game segments.
"If you get six out of 10 points every five-game segment, if you extrapolate that over 82 games, including the couple extra games you have in there, you're at about 98 points for the season, which generally is a playoff team," Blashill said. "It helps kind of give you a parameter of where you're at."
The Wings have a chance to reach that six-point benchmark Saturday in Montreal, the first of a quick two-game road trip (Sunday in Chicago).(c)2021 The Detroit News Distributed by Tribune Content Agency, LLC.