"It was a great pass," Dawes said. "I didn't even know if he saw me or not and he put it right on my stick and I just had to get it up over."
It was Dawes' fifth goal of the season and the first goal in 13 games.
"Obviously, whenever you're in a little bit of a slump, it's nice to get that one," Dawes said. "I haven't been getting to the areas that I need to. I need to get in close to the net because that's where I'm going to have my success and score the goals."
Daymond Langkow opened the scoring for the Flames late in the second period, and Keith Yandle tied it on a power play midway through the third.
In a dangerous rush with 2 minutes remaining, Kiprusoff kicked out a pad to stop Peter Mueller, then sprawled to deny Shane Doan on the rebound.
"We didn't play remotely good enough in the second period and, obviously, it's starting to get a little monotonous that we can't score goals and it starts with me," Doan said. "We're getting chances, we're getting opportunities. I get a chance with 3 minutes left to tie it up and I don't capitalize on it and that's the difference."
The Flames had lost four of their previous five games at home and are 7-5-0 at the Saddledome on the season.
Calgary (14-6-3) was playing its only home game in a stretch of 10. The Flames start a six-game trip Friday night in Detroit.
Phoenix was coming off a 4-0 loss in Edmonton on Monday night. ... Calgary had six former Coyotes in its lineup, and Phoenix had three former Flames.
Copyright by STATS LLC and The Associated Press
Arena: Scotiabank Saddledome Location: Calgary, Alberta
Referees: Eric Furlatt, Dennis LaRue Linesmen: Mike Cvik, Don Henderson
Attendance: 19,289 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
No scoring this period
Daymond Langkow (8)
Assists: Curtis Glencross, Eric Nystrom
Keith Yandle (4)
(Power Play) Assists: David Schlemko, Robert Lang
Nigel Dawes (5)
Assists: David Moss, Daymond Langkow