Kirk Maltby added an empty-net goal for Detroit. The Red Wings went 2-1-2 on their five-game trip and are 5-4-3 overall.
"We skated well and maybe for the first time all year we were a five-man unit and made some nice plays," Babcock said. "I liked the goals we scored and the way we went about our business tonight. It was impressive."
Daymond Langkow scored for Calgary, and Miikka Kiprusoff made 27 saves. The Flames dropped to 7-4-1 with their second straight loss. They went 3-2-0 on a five-game homestand.
"I thought we started out pretty good, keeping it simple, getting pucks deep," Langkow said. "We just got away from that. You can't do that against a team like that. We got away from what we need to do to be successful."
"I thought Connie had a decent game, but I thought both his wingers never played very well tonight," Sutter said. "The puck doesn't have legs on it, it isn't going to come to you. You've got to get after it and win battles. I just didn't think Jarome and Glennie had their better games tonight and that's the bottom line."
Iginla, who had five turnovers and finished with a minus-two rating, admitted he didn't have one of his better games.
"Before tonight I was feeling pretty good," he said. "I didn't have a very good game."
The Flames opened the scoring at the 14:43 mark of the second when Langkow swatted a loose puck out of the air and past Osgood, who stopped the initial wraparound attempt by Rene Bourque.
"Ozzy played real well but I thought we helped him out on a lot of the rebounds too," Detroit captain Nicklas Lidstrom said. "I thought we played with a lot more desperation too. As a group of five on the ice I thought we stayed together a lot better."
The Red Wings tied it just 35 seconds later when Stuart snapped a shot past Kiprusoff that went off sprawling Calgary defenseman Mark Giordano and into the top corner.
Holmstrom then took a pass from Pavel Datsyuk in the slot and snapped a heavy shot past Kiprusoff to make it 2-1.
Cory Sarich nearly put the Flames up 1-0 early in the second period when he redirected a cross-ice pass from Dustin Boyd off the post.
The Red Wings played without forward Valtteri Filppula, who broke his right wrist during Detroit's 6-5 loss to the Oilers on Thursday night. Also out of the lineup for the Wings were forward Johan Franzen (knee), defensemen Andreas Lilja (concussion) and Jonathan Ericsson (illness). ... Calgary defenseman Staffan Kronwall suited up against his older brother, Detroit's Niklas Kronwall, for the first time in his career. ... Detroit forward Todd Bertuzzi made his return to Calgary for the first time since playing last year for the Flames and heard a few boos from the crowd. "It didn't matter where we were at," Bertuzzi said. "We needed the win and we were very fortunate we came out and played one heck of a game tonight."
Copyright by STATS LLC and The Associated Press
Arena: Scotiabank Saddledome Location: Calgary, Alberta
Referees: Tim Peel, Kelly Sutherland Linesmen: Steve Barton, Pierre Champoux