The veteran linebacker picked off an errant pass by quarterback Drew Willy with 23 seconds remaining as Calgary edged the Winnipeg Blue Bombers 26-25 in front of 29,255 fans at McMahon Stadium.
"I just happened to be in the right place at the right time," said Simpson, who also had four tackles. "It felt good to be able to seal it for my team. We've been in this situation before. There was no panic by anybody on the team. We just keep fighting through. These are the games that you cherish because you realize how hard you fought to come back and get that win."
The Stamps (3-1) erased a 16-point deficit and won the game thanks to a 40-yard field goal by Rene Paredes, which was followed by Simpson's heroics.
"Fortunately we made a play at the end to seal the game," said Calgary coach and general manager John Hufnagel. "(Parades) hit a big one. We needed it."
Following the game-winning kick by Paredes at 12:46 of the fourth quarter, Winnipeg's Liram Hajrullahu had a chance to put the Bombers back out in front but he missed a 52-yard field goal attempt.
"I'm trying to do my best out there and fell a little short today," said Hajrullahu. "I'm going to learn from this and I'm going to be better for next week for my teammates and my coaches."
Bo Levi Mitchell, who started at QB for Calgary, threw a touchdown pass to Eric Rogers, while his backup Drew Tate had a rushing TD. Adam Thibault scored another touchdown for Calgary after picking up a blocked punt and running it into the end zone, while Paredes also kicked a pair of singles.
Willy threw a pair of long touchdown passes to Clarence Denmark and Darvin Adams, while backup quarterback Brian Brohm ran for another TD. Hajrullahu kicked a field goal and added two singles for the Bombers (2-2).
"It all stings," said Winnipeg coach Mike O'Shea. "It's sickening. We've got a team like Calgary on the ropes and we let them off the hook. We're not smart enough yet. We need to play smarter football and they all know it. The positive out of it is these guys expect way more out of themselves."
The Bombers jumped out to an early 8-0 lead thanks to a 93-yard single by Hajrullahu followed by a 75-yard touchdown catch by Denmark.
After Brohm plunged into the end zone for a one-yard TD to cap off an eight-play, 53-yard drive, Hajrullahu booted an 80-yard single to put Winnipeg up 16-0.
Late in the first quarter, Calgary's Randy Chevrier recovered a fumble by Bombers punt returner Troy Stoudermire at the Winnipeg 30-yard line.
Three plays later, Rogers caught a 19-yard touchdown pass from Mitchell, who hooked up with the same target in the end zone for a two-point convert.
The Stamps then settled for a single point early in the second quarter when Paredes missed a 26-yard field goal.
Adam Berger, who earlier forced the fumble by Stoudermire, then blocked a punt by Hajrullahu and Thibault promptly picked up the ball and ran it in for a 10-yard score. Parades made up for missing the convert by booting a 95-yard single on the ensuing kickoff to tie up the score at 16-16.
The Stamps took their first lead of the game at 12:35 of the third quarter when Tate ran for a one-yard touchdown to cap off an impressive 11-play, 107-yard drive. Running back Jon Cornish carried the ball four times for 66 yards on the drive.
The Bombers answered right back when Adams caught a pass from Willy at mid-field and ran the rest of the way for a 79-yard score. After Hajrullahu missed the convert, the Stamps were left with a one-point lead heading into the final quarter.
Hajrullahu then booted a 49-yard field goal at 8:07 of the fourth to put Winnipeg back up 25-23 before Paredes answered back with the game-winning kick.
Notes: Appearing in his first CFL game with the Stamps, rookie offensive lineman Karl Lavoie left the game with an apparent leg injury late in the first quarter and didn't return. … Stamps defensive back Brandon Smith played in his 100th CFL game.