Erik Gudbranson, Elias Lindholm, Matthew Tkachuk , Dillon Dube and Adam Ruzicka also scored for the homeside, who improved to 27-13-6 this season.
Toffoli's tally was an absolute gem and sent a jolt of electricity through the raucous crowd. Johnny Gaudreau flipped the puck high into the offensive zone on a line change and Toffoli, who had just come out, chased it down, cut in front of two defenders and on one leg, put a backhand home at 11:04 of the third period.
The C of Red acknowledged the debut goal with a lengthy 'Tyler Toffoli' chant after the ensuing faceoff and later, again, after a TV timeout.
Gaudreau had a pair of assists in the win and is now just one away from passing Mark Giordano (366) for fifth in franchise history.
The Flames current run of consecutive victories in the longest in the NHL right now as they continue to get contributions from up-and-down their lineup, outscoring the competition 35-8 during that span.
Dan Vladar, who last played on Feb. 1 coming in to backstop the third period in a come-from-behind win over the Dallas Stars, got the victory in his first start since Jan. 7.
He was sharp when he needed to be, turning aside 18 shots as he improved to 7-3-1 on the season. Elvis Merzlikins got the start at the other end of the ice, making 35 saves.
The last time these two clubs met was back on Jan. 26 in Ohio when the Flames blanked the Blue Jackets 6-0 as they fired a franchise record 62 shots on net.
They didn't waste too much time picking up right where they left off.
Erik Gudbranson snapped a long-distance wrist-shot through traffic at 17:50 that beat Merzlikins just 2:10 in, Milan Lucic getting the helper.