The Flames took a 1-0 lead at 9:41 of the first period. Farabee came off the bench with speed, split two Anaheim defenders and redirected a pass from Ryan Lomberg into the net.
Farabee credited teammate Adam Klapka with making a line change at the right time.
"He saw we had possession and he made the decision to come off, and it let me come on the ice with a lot of speed and 'Lombo' made a great pass," Farabee said. "If he doesn't change at that point, I don't score."
Cooley made his 14 saves in the first period, with his final one coming against a breakaway by Ryan Poehling at 17:11, three seconds after an Anaheim penalty expired.
"I thought we were really good," Cooley said. "We generated a lot of chances. Their goalie made really, really good saves. I thought we could have scored five goals out there tonight."
Gauthier tied it 1-1 at 11:14 of the second period. Cooley stopped two of Gauthier's shots before the Ducks forward banked the puck off the goalie's shoulder from below the goal line. The puck popped up in the air, slid down Cooley's back and rolled into the net.
“Their goalie played a really good game," Gauthier said. "We had a lot of shots on him."
Sharangovich put Calgary back ahead 2-1 with a power-play goal at 16:10, scoring bar down with a shot from the inside edge of the right face-off circle that made it through traffic and over Dostal's right shoulder.
Gauthier tied it 2-2 on a power play at 10:41 of the third period with a one-timer from the right circle that beat Cooley to the glove side off a touch pass from Jackson LaCombe.
"We're ready to play 60 minutes," Dostal said. "We are always there, always ready to play for a whole 60 minutes, and we have young legs, young guys and we skated the whole game. So that's been our strength, I believe."