Clarke MacArthur scored on a tip in 13 minutes into the third period after Jared Cowan had given the Senators a 4-3 lead a little over a minute into the third period.
Turris scored into an empty net and Robin Lehner made 37 saves allowing the Senators (31-29-14) to win back-to-back games on home ice for the first time since they won three straight in late December and early January.
The Flames could not have played a much better period than they did in the second as they outshot the Senators 21-9, but the best they were able to do after taking a 3-2 lead was go into the second intermission tied 3-3.
Ottawa native Byron scored four minutes into the period for the Flames to tie the game as he corralled a rebound in the slot and put a shot into the top corner.
It was only Byron's second career game in his hometown and he has a goal in each of those games. He scored his first goal in his second NHL game in early 2011 when he was a member of the Buffalo Sabres.
A little more than three minutes after Byron tied the game, former Ottawa 67's standout Sean Monahan scored to give the Flames a 3-2 lead as he picked the corner over Lehner's left shoulder.
The goal was the 20th of the season for Monahan, making him the third rookie this season to reach that plateau along with Nathan MacKinnon of the Colorado Avalanche (23) and Tyler Johnson of the Tampa Bay Lightning (22).
The Senators had gone into the third period with a 2-1 lead as Michalek sandwiched goals around one from Stajan.
Michalek opened the scoring when he redirected a point shot from Erik Karlsson past Ramo at 10:42.
Less than three minutes later though, Stajan jumped into the slot and buried a pass from behind the net past Lehner.
Michalek re-established a one-goal lead for the Senators thanks to some terrific patience from Jason Spezza.
The Senator's captain moved around a sliding Calgary defenceman behind the goal-line, cut back out in front and slid a backhand pass that Michalek buried for a 2-1 lead.
Notes: Cody Ceci, Bobby Ryan and Colin Greening were scratches for the Ottawa Senators while scratches for the Calgary Flames were Bryce Van Bradrant, Ladislav Smid, Dennis Wideman, Kenny Agostino, David Jones, Ben Hanowski and Markus Granlund. ...The game was the first Ceci has missed in his career since he was called up from Binghamton in early December. He played in 41 straight games. ... The Flames have played in 45 one-goal games this season and remain one shy of establishing a new franchise record. Their record in those games is 22-16-7.