Joel Farabee also scored for the Flames (7-13-3) and Nazem Kadri had two assists. Making consecutive starts for the first time this season, Cooley made 28 saves. He also made 28 saves in a 6-2 win for the Flames at the Buffalo Sabres on Wednesday.
Kadri scored the deciding goal in the fourth round of the shootout before Cooley stopped Roope Hintz to preserve the win.
Jason Robertson had a goal and an assist for the Stars (13-5-4) and Hintz also scored. Casey DeSmith made 31 saves.
Coronato gave the Flames a 1-0 lead at 11:41 of the first period with a power-play goal. He took a pass from Kadri behind the goal line and then went backhand to forehand while spinning around to the front of the net before sneaking a shot through DeSmith’s pads.
Coronato left the game late in the second period after taking a hit from behind into the boards from Mikko Rantanen, who was assessed a five-minute major for boarding and a game misconduct. Although he wasn’t on the bench to start the third period, Coronato later returned with stitches across the bridge of his nose.
Farabee put the Flames up 2-0 with a power-play goal at 1:50 of the third period when he redirected a point shot by defenseman Rasmus Andersson past DeSmith. Andersson extended his point streak to four games (seven points; two goals, five assists).
Robertson cut Calgary’s lead to 2-1 at 6:44 when his shot from the top of left circle beat Cooley to the short side. Robertson extended his goal-scoring streak to a career-best six games (10 goals).
Hintz tied the game 2-2 at 16:53 when he took a pass from Robertson in the slot and snapped a shot to the top corner over Cooley’s blocker.