Girard scored from the left face-off circle on a 2-on-1 after receiving a pass from Evan Rodrigues for his first NHL overtime goal.
"We've been fighting, grinding out wins, low-scoring games," Rodrigues said. "Even when we're down, guys believe we can come back."
Mikko Rantanen had a goal and an assist, and Alexandar Georgiev made 37 saves for the Avalanche (19-11-2), who have won four in a row, including 1-0 in a shootout against the New York Islanders on Monday, and 2-1 in overtime against the Montreal Canadiens on Thursday.
"It feels awesome," said Georgiev, who made his fifth straight start. "Nothing came easy the last few games. Every win felt really special because it's tie games every time. It's overtime or one-goal game or shootout. Awesome job by the guys sticking with it and having the championship character."