The trio kept pressing, even after Wyatt Johnston got the home side on the board.
Farabee knocked the puck down in neutral ice, then channeled his inner Lionel Messi, back-heeling the disc across to Backlund who carried it down the right wing to start a 2-on-1 rush, forcing Oettinger into another tough stop with just over four minutes on the clock.
The Flames newcomer kept making an impact in period three, this time playing distributor, setting up Coleman for a dangerous slot opportunity that skipped away, and almost finding a lunging Backlund at the back post on back-to-back shifts.
The home side pushed for an equalizer though, outshooting Calgary 7-1 through the first half of period three.
Jason Robertson found it, tying the score at 2-2 with a low shot from the left circle at the nine-minute mark.
From there, the game got heavier, harder along the walls.
The type of game that suited Martin Pospisil, who forced two turnovers, the latter leading to a chance from Yegor Sharangovich from in tight that nearly broke the stalemate inside the final five minutes.
At the other end, Rasmus Andersson got his body in front of a clear-cut chance off the stick of Matt Duchene with just over three minutes to play, saving Vladar from having to make a difficult save as the two teams skated the remainder of the 60 regulation minutes with nothing between them.
Vladar made his best stop of the evening just under two minutes into overtime, denying Johnston's low shot with the left pad after following him across the crease from right to left.
Nazem Kadri was set up beautifully a minute later in the Dallas zone, gliding through the slot before releasing a hard shot, but his effort found iron and stayed out.
Robertson ended the game with 43 seconds remaining in the frame, tucking home his second goal of the night to give Dallas a 3-2 triumph.
