A tripping minor to Ottawa defenceman Chris Wideman had expired seconds before the go-ahead marker.
The Sens were bossing the shot clock, 26-12, but the Flames came closest to scoring before the period ended, Dennis Wideman's set-it-up-on-a-tee slapper from the high slot, deflecting off a thicket of bodies and nestling against the post.
"We were out played; I didn't really like our game," assessed Glen Gulutzan. "I thought for five minutes in the first we had a good push and about five minutes in the second. The Senators controlled probably fifteen to twenty minutes of those periods pretty handily."
"In this league you are going to have nights where you are going to face a barrage and teams are going to have jump on you. I don't know why [that was the case] tonight."
Calgary had opened brightly, Hamilton firing a wrist shot from the right point that sailed through, short side, at 5:24 of the first period.
"It's good. I think just sticking to our game plan is working right now," Hamilton said. "We have to keep it going obviously. It's nice to be able to do it at home. We've got another home game now and another road trip so we've just got to keep going."
The Flames then ran smack-dab into a bit of penalty trouble. Four seconds after Matthew Tkachuk had been incarcerated for latching onto Erik Karlsson's stick, the two-time Norris Trophy winner wired a shot from the blueline, dead centre, past a screened Elliott.
Calgary's second minor of the period, Bennett for tripping, also wound up biting the homesteaders, a shot from Sens' Kyle Turris ricocheting off a Dennis Wideman shinguard and in.
Ottawa rattled off the final nine shots of the period.
NOTES:Scratched for the Flames was Nicklas Grossmann, Freddie Hamilton and Brett Kulak. Jyrki Jokipakka drew into the lineup in favour of Grossmann, who suited up in Tuesday's 4-1 win over the St. Louis Blues … Thomas Chabot was the lone scratch for Ottawa.
UP NEXT: The Flames will host the Washington Capitals at Scotiabank Saddledome on Sunday (7:30 PM MT; Sportsnet, FAN 960).