Phoenix dominated most of the first two periods, going up 2-0 on Radim Vrbata's 200th career goal and Ribeiro's first of the night.
Rob Klinkhammer added an empty-net goal for Phoenix, which has earned 12 of a possible 14 points in its past seven games. The Coyotes, with 16 points (6-2-2), are off to their best start since opening the 2000-01 season 7-1-2.
Calgary's Jiri Hudler had an assist to extend his season-opening points streak to nine games.
Phoenix's Mike Smith stopped 22 shots, including 12 in the third period.
The Coyotes wanted to jump on the Flames early after they played the night before in Los Angeles and did just that with a power-play goal midway through the first period. Keith Yandle set it up by faking a shot and passing to Vrbata, who gathered the puck and wristed it past Joey MacDonald from the right circle for his fifth goal of the season.
Phoenix was at its defensive best early on as well, blocking shots and pushing the Flames toward the boards while holding them to three shots in the first period.
Then it was Ribeiro's turn.
He got off to a slow start with Phoenix after signing a four-year, $22 million contract, failing to register a point his first three games.
Since then, Ribeiro has been the playmaking force the Coyotes expected, setting up and scoring goals in every game since, including two goals to Phoenix's comeback, 5-2 victory over Detroit on Saturday.
He kept the points streak rolling in the second period, raising his stick waist high deflect a shot by Mikkel Boedker past MacDonald for a 2-0 lead.
Calgary finally showed some life late in the second period, starting a rush with a Coyotes' turnover that led to Stempniak's goal on a rebound, cutting Phoenix's lead to 2-1.
The Flames kept it rolling to open the third, turning a turnover by Phoenix into a breakaway for Colborne, who used a deke to get Smith down before flipping in his first of the season.
Ribeiro came through again less than three minutes later.
Set up to the right of MacDonald, he ripped a one-timer from a tough angle on another crossing pass from Yandle, putting the Coyotes up 3-2 with his fifth of the season.
NOTES: Both teams played without their captains. Phoenix's Shane Doan was out with a lower-body injury and Calgary's Mark Giordano was scratched after leaving during pregame warm-ups. ... The Coyotes recalled F Brandon Yip before the game and sent F Tim Kennedy to Portland of the AHL before the game. Yip started in place of Doan. ... Hudler has 12 points in nine games this season.