Rashaun Simonise gave the host Dinos a 17-0 lead in the first quarter when he scored on an 80-yard punt return on a snowy turf in Calgary.
Andrew Buckley threw two touchdown passes for Calgary, a 15-yarder to Brett Blaszko that made it 10-0 in the first quarter, and a 24-yarder to Jake Harty in the third quarter, making it 27-3.
Buckley finished the game completing 18 of 27 passes for 211 yards, with no interceptions.
Mercer Timmis and Doctor Cassama scored the other Dino touchdowns in the fourth quarter. Timmis scored on a 41-yard run, and Cassama, on a 71-yard interception. Timmis finished the game with 16 carries for 139 yards.
Calgary running back Cuong Thai Lieu also got into the action with 93 yards on 12 carries.
"This is in the top two or three of my career," said Calgary head coach Blake Nill, who will be taking the Dinos to the Vanier Cup for the third time in five years. "This is so special right now, because these kids really haven't proven anything prior to coming here, they don't understand what they just accomplished.
"It's really just been a terrific year up to this point.
Western went into the game with the country's top offence, but quarterback Will Finch was hassled relentlessly by a physical Calgary defence.
Finch was injured in the opening half, favouring his hip throughout the game. After being helped to the dressing room in the late stages of the second quarter, he reappeared in the third, but couldn't get the passing game together, completing just nine of 20 passes for 105 yards and an interception.
His replacement, Blake Huggins, fared little better, going 1-for-11 for 1 yard and one pick.
Mustangs running back Yannick Harou ran 17 times for 87 yards.
Johnny Mark booted three field goals for the Dinos, and Liriam Hajrullahu provided all of the Western points with a 26-yard field goal in the second quarter.
"It's one of those games where everything that could go wrong did go wrong," said Mustangs coach Greg Marshall. "It started with Will right off the get-go, he kind of pulled that hip and he wasn't the same.
"They gave it to us on special teams, they gave it to us on defence, and we dropped the ball. Sometimes when things go sideways like that it's hard to get it back on the rails. Credit to Calgary, they did a great job."
Earlier, Laval downed the Mount Allison Mounties 48-21 to earn their fourth consecutive trip to the Vanier Cup.