Montreal scored 13 points in the fourth quarter, including a three-yard touchdown run by Brandon Whitaker and a 17-yard field goal by Whyte which put the Alouettes up 28-26 at 12:09.
Hamilton's Luca Congi kicked his fifth field goal of the game with 1:22 remaining, a 47-yarder to put the Tiger-Cats up 29-28.
Chris Williams tied a CFL record with his fifth kick return touchdown of the season for Hamilton in the second quarter.
Montreal quarterback Anthony Calvillo celebrated his 40th birthday with a milestone touchdown pass to S.J. Green, hitting the Alouettes' receiver in the end zone for a 10-yard strike 9:53 into the second quarter.
Calvillo's 436th career touchdown pass moved him past Warren Moon into second place all-time in pro football history. Moon threw 435 touchdown passes, including 144 with Edmonton from 1978-83. Brett Favre threw 508 touchdown passes, all in the NFL.
Williams returned Whyte's punt 70 yards for his fifth kick return touchdown of the season, tying Henry "Gizmo" Williams' CFL single-season record set in 1991.
It was Chris Williams' fourth punt-return touchdown of the season. He also returned a missed field goal for a touchdown. Gizmo Williams still holds the record for most punt-return touchdowns in a season with five.
Former Alouette Avon Cobourne's 15-yard touchdown reception from Henry Burris gave Hamilton a 26-18 lead 2:57 into the fourth.
Whitaker's three-yard run at 7:14 helped bring Montreal within 26-25. Whyte hit his second of three field goals with 2:20 left, a 17-yard kick as the Alouettes settled for a 28-26 lead after Calvillo was sacked by Greg Peach for a seven-yard loss with Montreal on the three-yard line.
Adrian McPherson scored on a one-yard quarterback sneak to give Montreal its first lead, 18-16, 10:53 into the third quarter.
Green nearly had a second touchdown reception but he was downed inches short of the goal-line just before McPherson's quarterback sneak.
Alouettes free safety Kyries Hebert laid out Hamilton's Onrea Jones with one of the most devastating blocks of the season. Montreal's Jerald Brown intercepted Burris in the third quarter and Jones was in pursuit when Hebert caught him with his head down, sending the Tiger-Cats slotback flying backwards.
Notes: Quebec's Olympic medalists were introduced to the crowd at half-time, including Emilie Heymans, who won a bronze with Jennifer Abel in synchronized springboard to become the first diver in Olympic history to win medals in four straight Games.