Tissot collected his first career goal in the 87th minute of the match to help lift the visiting Impact to a 2-2 tie with the Chicago Fire.
Tissot, who had appeared in just two matches entering Saturday, scored on a short header in a flurry in front of the Fire goal late in the Major League Soccer clash at Toyota Park.
The tie gave Montreal (13-9-7, 46 points) a valuable road point as it remains in third place in MLS' tight Eastern Conference playoff race.
"If I can have three points, that's better," Impact coach Marco Schallibaum said. "(But) when you see the game and you're behind 2-1 and you come back to get the (tie) I'm happy."
The deadlock snapped the Impact's two-game losing streak while Chicago (11-12-7, 40 points) fell to seventh place, two points out of the fifth and final conference playoff berth.
Chicago forward Mike Magee scored in the 57th minute as he slipped through two defenders and skipped a short shot past Impact goalkeeper Troy Perkins to tie it at 1-1.
He struck again in the 73rd minute when Perkins tried to clear the ball. Magee aggressively challenged Perkins, picked up the loose ball and hit the back of the net for his 18th goal of the season.
Magee just missed a hat trick when a penalty kick in the 79th minute hit the left post.
"That's a situation where I've got to put that away for the team," Magee said. "That's a big goal. ... It wasn't my time."
MLS scoring leader Marco Di Vaio gave the Impact a 1-0 lead in the 25th minute when he slipped between two Fire defenders and launched a 12-yard shot past Chicago goalkeeper Sean Johnson.
The goal was Di Vaio's 19th of the season and third career strike against Chicago.
"The second half we didn't have so much energy as in the first half and that comes from more pressure from Chicago," Schallibaum said. "They made it 1-1 and then the second (goal) was a present on our part. But we didn't give up."
Impact midfielder Felipe Martins — the team's No. 2 scorer with five goals — sat out due to excessive caution accumulations. Fire defender Bakary Soumare was out due to a red card issued last Saturday at Columbus.
Consecutive losses at Stade Saputo to Columbus and Vancouver left the Impact still in the playoff picture but not as the MLS Eastern Conference leaders the Impact were a few weeks ago.
The Impact, who have five regular season games remaining, travel to Houston on Friday and return home to host New England on Oct. 12.