After Jagr's rebound resulted in Mark Jankowski's first NHL goal to open the scoring 9:15 into the first period, the future Hall-of-Famer showed the type of finish around the net that has got him 766 career goals, second only to Wayne Gretzky.
Breaking up ice on a 2-on-1 with Johnny Gaudreau, Jagr got himself open, took a cross-ice pass and after patiently waiting for Petr Mrazek to go down, neatly snapped a shot past the Red Wings goaltender.
It was Jagr's first two-point game with the Flames, who signed the 45-year-old as a free agent on Oct. 4. Jagr was playing in his second-straight game after missing six with a groin injury. He has four points in seven games this season.
Gaudreau scored a pair of goals, including an empty netter, Micheal Ferland and Matthew Tkachuk also tallied for Calgary (9-7-0). The Flames have won four of their last five. Gaudreau's three-point night extends his point-streak to six games.
Martin Frk, Frans Nielsen and Anthony Mantha had goals for Detroit (8-8-1).
Up 2-0 after the first period, the Flames extended their lead to three goals at 6:02 of the second on a nice play by Ferland, who split the Detroit defense then scored on a pretty deke to his forehand.
Ferland has goals in three straight games and in four of his last five as he continues to impress on the right side of the Flames' top line with Gaudreau and Sean Monahan.
Frk's power-play goal at 8:43 got Detroit on the scoreboard, but Tkachuk's deflection out of mid-air off Brett Kulak's point shot restored Calgary's three-goal cushion.
The best of Mike Smith's 39 stops in a loosely-played game by Calgary defensively came early in the second. After Gaudreau had the puck stolen by Dylan Larkin in his own end, Smith bailed him out by robbing Larkin with a spectacular glove save.
Mrazek, who recorded a 36-save shutout over Edmonton in his last start, turned aside 28-of-33 shots.
Notes: Rookie D Rasmus Andersson, 21, made his season debut for the Flames with veteran Matt Bartkowski a healthy scratch. Andersson finished a plus-two in his second career game. ... The two teams will meet again in Detroit on Wednesday... The Red Wings play 13 of their next 15 games at the new Little Caesars Arena.
Red Wings: host Columbus on Saturday.
Flames: host St. Louis on Monday.