Olli Jokinen and Curtis Glencross each had a goal and an assist for Calgary, which has won eight of nine. Since losing 6-0 at home to Minnesota on Jan. 19, the Flames have gone 8-0-1 to climb back into contention in the Western Conference playoff race.
Playing in his 800th NHL game, Robyn Regehr chipped in with two assists.
Chris Kelly and Chris Campoli scored for Ottawa (17-30-8), which led 2-1 after the first period. The Senators have lost five straight in regulation and 11 overall (0-9-2). Ottawa is 1-13-4 in its past 18 games.
Miikka Kiprusoff made his eighth straight start for the Flames and stopped 24 shots to improve to 24-18-3. Ottawa rookie Robin Lehner made 30 saves in the loss.
The Flames went 3 for 5 with the man advantage and killing all three Ottawa power plays.
Thanks to an early power play, the Flames put on some great pressure but were kept off the score sheet due to several nice saves by Lehner. Shortly after stopping a shot through traffic by Jarome Iginla, Lehner stacked his pads to thwart Brendan Morrison.
Jackman opened the scoring at 8:40 of the first when the puck deflected off him and into the net after Lehner made a blocker save to stop Niklas Hagman's shot.
Just 37 seconds later, Kelly tied it when he took a pass from Jarkko Ruutu and snapped a shot to the short side past Kiprusoff.
The Senators went ahead 2-1 two minutes later when Campoli took a point shot that hit Kiprusoff before bouncing up and over the Calgary goalie.
The Flames tied it again during a second-period power play when Jokinen redirected a pass from Glencross past Lehner.
Jokinen returned the favor a short time later when he sprung Glencross on a breakaway. Glencross wired a perfect shot into the top corner over Lehner's outstretched glove.
The Flames took a 4-2 lead at 8:36 of the third when Babchuk fired a point shot past Lehner, who was screened by David Moss.
Jackman rounded out the scoring on the power play when he tapped in a loose puck behind Lehner, who stopped Iginla's original shot before it trickled past him.
Notes: Hagman returned to Calgary's lineup after missing three games with a lower body injury. ... Alex Tanguay, who three goals and six assists in Calgary's previous eight games, sat out because of a neck strain. ... With D Adam Pardy out of Calgary's lineup due to an upper body injury, Brendan Mikkelson played for the first time since Jan. 15 - a span of 10 games.