Calgary was up 17-7 at halftime and extended that lead to 13 points when Rene Parades kicked a 20-yard field goal with 4:20 left in the third quarter.
Before that drive stalled, Stampeders No. 1 quarterback Bo Levi Mitchell completed 10 straight passes to tie for the third longest completion streak in Grey Cup history.
The only other highlight of the quarter came when Hamilton defensive end Justin Hickman laid out Calgary punter Rob Maver on a return.
Parades took over punting duties the rest of the way for Maver, who left with an injury to his abdomen.
Calgary led 7-0 after the first quarter and doubled that lead when Tate scampered over the goal-line 48 seconds into the second to cap a 10-play, 66-yard drive led by Mitchell that was aided by a pass interference call in the end zone on Tiger-Cats defensive back Brandon Stewart.
Hamilton had a chance to get on the board later in the quarter, but Justin Medlock's 26-yard field goal was blocked by Calgary defensive lineman Demonte' Bolden.
Parades then stretched the advantage to 17-0 with an 11-yard field goal at 12:43 after the ensuing Calgary drive of eight plays and 87 yards stalled deep in Hamilton territory.
The Stampeders did a good job containing Tiger-Cats returner Brandon Banks in the first half, but the speedster got behind the Calgary defence for a 45-yard touchdown on a pass from Zach Collaros that cut the deficit to 17-7 with 1:21 left in the half.
Tate came in for the short yardage plunge over the goal-line with 9:48 gone in the opening quarter to finish off a five-play, 55-yard drive that included a 28-yard pass from Mitchell to wide receiver Eric Rogers.
Hamilton punted on its first four drives and were lucky the deficit wasn't any wider after running back Nic Grigsby's fumble was recovered by Tiger-Cats offensive lineman Brian Simmons for a 29-yard loss.
At least two Calgary players had their hands on the ball before Simmons fell on it for Hamilton, which had just four net yards of offence in the quarter.
Attendance at B.C. Place Stadium was 52,056 fans — 1,423 short of capacity.
The Stampeders finished the regular season 15-3 before downing the Edmonton Eskimos in last weekend's West Division final, while the Tiger-Cats topped the Montreal Alouettes to win the East following a 9-9 campaign.
Hamilton lost last year's Grey Cup to the Saskatchewan Roughriders in Regina and have not won the big game since beating Calgary in Vancouver back in 1999.
The Stampeders last won in 2008, but lost the 2012 final to the Toronto Argonauts.