Calgary has now picked up a point in 13 straight home games, dating back to Jan. 18. They are 12-0-1 over that span.
Johnny Gaudreau - who notched the OT winner in Colorado Saturday night - also scored, while Jacob Markstrom made 27 saves as the Flames improved to 34-14-7.
The victory kicked off a hectic run of five games in seven nights for Calgary, which will be right back at it tomorrow night when they host the Capitals.
Edmonton had prevailed in the first two of four meetings between the bitter archrivals this season.
It was a hard-fought game, as the Flames held Edmonton's dynamic duo of Connor McDavid and Leon Draisaitl without a point in the win.
Toffoli had the first Grade-A chance of the game, coming just past the midway mark with the Flames killing a penalty to Mikael Backlund.
He skated in on a breakaway and cut in from the left wing and tried to tuck a backhand around Mikko Koskinen's outstretched pad but it went off the post.
Calgary went back on the PK five minutes later, this time Backlund getting the best look when he held the puck on a 2-on-1 with Elias Lindholm and fired it off the post.
Markstrom made a stellar stop just over two-and-a-half minutes into the second period, coming across his crease to make a lunging blocker stop on Brad Malone who took a cross-ice pass all alone in the slot.
The Flames killed off the Oilers third powerplay of the game and earned one of their own not long after, and made good.
Gaudreau passed to Matthew Tkachuk to the left of Koskinen and he tried his patented between the legs shot, but the puck skirted through the blue paint onto the stick of Toffoli, who snapped it upstairs at 6:07.
