Running back Jon Cornish scored two of those touchdowns, one rushing and one receiving. He also had a two-point convert catch to tie the game late in the fourth quarter.
Stampeder quarterback Bo Levi Mitchell threw touchdown passes to Sederrik Cunningham and Brad Sinopoli. He went down awkwardly on his left leg with six minutes remaining in the game.
Mitchell was replaced by Drew Tate, who tied the game with a touchdown throw to Jabari Arthur and the two-point convert toss to Cornish.
Cornish, the CFL's most outstanding player in 2013, posted over 100 rushing yards for a third straight game in front of an announced 28,607 at McMahon Stadium. Calgary kicker Rene Paredes was good on his lone field-goal attempt.
Calgary stayed atop the CFL and West Division standings at 10-1. The Argonauts were tied for the East Division lead with Montreal at 3-8.
Toronto quarterback Ricky Ray fumbled the ball on the Argos final drive and turned the ball over on downs with nine seconds remaining.
Ray threw touchdown passes to Spencer Watt, Jason Barnes, Trent Guy and Andre Durie for a 29-10 lead after the first half. Swayze Waters had a field goal in the second half.
Argos receiver Chad Owens, the CFL's MOP two years ago, didn't play in Calgary because of a leg injury. He's expected back in the lineup Friday against the B.C. Lions in Vancouver. Durie played Saturday after missing eight games with a broken collarbone.
Cornish put Calgary up a converted touchdown at 13:12 of the fourth quarter with a 30-yard scoring run.
Toronto led 33-25 on a 66-yard punt single by Waters early in the fourth quarter, but the Argos turned the ball over at midfield on slotback LaVonn Brazill's second fumble of the game.
Mitchell was injured on the ensuing drive. Tate finished it with pass to Arthur in the end zone followed by a two-point convert pass to Cornish.
Calgary trailed by a converted touchdown at 9:53 of the third quarter after Mitchell's 14-yard touchdown toss to Brad Sinopoli and a Paredes convert.
Waters was good from 36 yards to pad Toronto's lead to 32-10 early in the second half, but Cornish's 79-yard touchdown dash at 6:10 breathed life into Calgary's offence.
Toronto's roughing-the-passer penalty gave the Stampeders a second chance at a two-point convert, which Matt Walter completed with a two-yard dash.
Trailing 29-3, Mitchell connected with Cunningham on a 12-yard strike in the final minute of the first half for Calgary's first touchdown of the game.
Barnes beat Calgary cornerback Fred Bennett to the end zone for Ray's 27-yard strike at 10:16 of the second quarter.
A Jermaine Gabriel interception and a Cornish penalty for unnecessary roughness put Toronto on Calgary's 19-yard line earlier in the quarter. Calgary left Watt uncovered in the end zone for a two-yard toss from Ray at 5:47.
The Argos turned the ball over fumbling the opening kickoff, but recovered to score on their next two possessions. Waters added an 80-yard single to make it 15-3 for the visitors after the opening quarter. It was the first time in five games Calgary trailed after a quarter.
Ray was 8-for-8 in passing for a combined 155 yards on the first two touchdown drives, capped with an 11-yard touchdown throw to Guy and a 15-yarder to Durie.
Brazill fumbled the opening kickoff with Adam Berger recovering the ball on the Argonauts' 29-yard-line. The hosts converted the turnover into a 28-yard field goal from Paredes.
Notes: Stampeder defensive ends Charleston Hughes and Ben D'Aguilar, receiver Marquay McDaniel and defensive tackle Demonte Bolden did not finish the game because of injuries . . . The Argos will stay and practice in Calgary next week in preparation for Friday's game in Vancouver.