Yamamoto became the first pitcher since Johnny Cueto (2015) to throw a complete game in the World Series and the first pitcher to throw back-to-back complete games in the postseason since Curt Schilling in 2001 - who went on to win World Series MVP.
The Dodgers' star pitcher retired 20 straight batters to end the game, including striking out the side in the top of the eighth inning.
Yamamoto would finish the game himself after giving up just one run on four hits with eight strikeouts and zero walks on 105 pitches
He finished the ninth inning by forcing Vladimir Guerrero Jr. to ground out, Alejandro Kirk to line out to centre, and getting Daulton Varsho to pop up.
The first complete game from Yamamoto came during Game 2 of the National League Championship Series against the Milwaukee Brewers.
Yamamoto has now tossed 18 innings in his past two starts, giving up two runs on seven hits with 15 strikeouts and one walk.
Full game recap
Dodgers 1-1 Blue Jays
Dodgers got on the board first at the start of the game thanks to a Will Smith two-out RBI single in the top of the first inning to bring Freddie Freeman to the plate.
Despite getting into a tough situation with players on first and third, Yamamoto got out of the jam in the bottom half of the innings thanks to a pair of strikeouts and a nice snag from Freeman at first.
Blue Jays 1-1 Dodgers
After a scoreless second inning, the Jays tied things up in the bottom of the third.
Blue Jays catcher Kirk popped a one-out sacrifice fly to left-center field to bring home George Springer from third to tie the game up.
Dodgers 3-1 Blue Jays
In the seventh inning, the Dodgers retook the lead and it started with a pair of solo home runs.
Will Smith smashed his first home run of the postseason into the second deck of the Rogers Centre off Jays starting pitcher Kevin Gausman.
Then Max Muncy doubled the team's lead shortly after with his second home run of the postseason, effectively ending Gausman's night.
The Blue Jays starter got through 6.2 innings of work, giving up three runs on four hits with six strikeouts and no walks.
Dodgers 5-1 Blue Jays
Toronto relief pitcher Louis Varland came in to relieve Gausman, but immediately got in trouble after loading the bases.
So the Blue Jays made another change on the mound, bringing in Jeff Hoffman. LA's Andy Pages would score from third off a wild pitch from Hoffman to put the Dodgers up 4-1.
Hoffman would intentionally walk Freeman to load the bases for a possible double play opportunity with one out. But Smith would drive in a run with a groundout before Hoffman was able to get out of the inning.
Dodgers finished the game going 1-for-3 with runners in scoring position, Blue Jays 1-for-2.
Game 3 of the World Series heads to Los Angeles on Monday, October 27th.