Dinos running back Mercer Timmins had three touchdowns while teammate Jimmy Underdahl ran in another to improve the No. 3 ranked Calgary team to 7-0 on the season.
Quarterback Andrew Buckley threw for 235 yards and zero touchdowns, and kicker Johnny Mark added 11 points on two field goals and three singles.
Kolten Solomon was the top receiver for the Rams (2-5) with 164 yards and a TD.
Calgary jumped out to an early 9-0 lead on Underdahl's 32-yard touchdown run and two rouges in the first quarter. The Dinos led 22-10 at halftime, thanks in part to Michael Schmidt's 56-yard kickoff return for a score.
Regina battled in the third, scoring 11 points on two safeties and an 82-yard touchdown pass from Shutter to Solomon, to pull within seven points heading into the final quarter.
But Calgary responded with 17 points in the fourth, including two rushing touchdowns from Mercer to put the game out of reach.
Richard Sindani scored a touchdown for Regina on a 25-yard pass from Shutter with 49 seconds remaining in the game.
Bisons 33 No. 7 Huskies 26
At Saskatoon, Jordan Yantz threw four touchdown passes including one to Alex Vitt late in the fourth quarter to send Manitoba (4-3) past Saskatchewan (4-3).
Mounties 27, Huskies 24
At Halifax, Brandon Leyh threw a 57-yard pass to Troy Trentham in the fourth quarter to put Mount Allison (2-4) ahead of Saint Mary's (4-2) for good.