Oliver Kylington also scored for the red-hot Flames, who have gone 7-0-1 in their last eight games.
Ryan Nugent-Hopkins and Milan Lucic had goals for the Oilers, who had won back-to-back games before playing Calgary.
With Calgary leading 3-1, Edmonton pulled within one with a power-play goal 4:16 into the third period when Lucic tipped Jesse Puljujarvi's shot past David Rittich.
But the Flames regained their two-goal lead with 5:45 remaining when Backlund picked off a pass and scored his 11th.
Monahan added a power-play goal at the 16:03 mark to put the game away with his 27th of the season.
There was no scoring in the first period, although the Flames came close on the power play with 1:10 remaining. A shot by Gaudreau hit the post and then Mikko Koskinen's back and was headed into the net before the Oilers goalie made an acrobatic behind-the-back save with his glove, a play that stood a video review.
Gaudreau broke the scoreless deadlock just 44 seconds into the second period as he swung wide before putting the puck through Koskinen's legs for his 29th goal of the season and his 17th in his last 19 games.
Calgary took a 2-0 lead with a power-play goal in the middle of the period when Giordano smacked in a shot in during a scramble out front.
The Flames added to their lead late in the period on a one-timer by Kylington.
Edmonton finally got on the board with 18 seconds left in the second when Nugent-Hopkins scored his 16th while the teams were playing four aside.
NOTES: It was the third of four meetings this season between the Alberta-based rivals. Each team came in having won in its home arena, with the Flames beating the Oilers 4-2 in Calgary and Edmonton winning 1-0 at Rogers Place.
Flames: host Carolina on Tuesday night.
Oilers: host Carolina on Sunday night.
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