The Boston Red Sox star hit a huge home run in the seventh inning after Japan's bats - so destructive in the WBC thus far - froze up against Australia.
The Aussies, who led after an errant throw allowed Aaron Whitfield to score in the sixth, restricted Japan to just three hits early on.
Starter Connor MacDonald was dealing, throwing three innings of one-hit ball to give his side a chance of upsetting the giants of Pool C.
Whitfield's opportunistic run then lifted the hopes further, but Japan were ready to pounce.
Yoshida was the man to turn the game. He sent the ball 394 feet to cash in a pair, and from there, the home side were in control.
Pinch hitter Terauki Sato came off the bench in the eighth to spray a double down the left field line, scoring Sosuke Genda from third to give Japan a two-run lead. They then loaded the bases before Seiya Suzuki drew a walk to force in a run and make it 4-1.
Australia would try to rally late - both Alex Hall and Rixon Wingrove would homer in the ninth, but it was just not enough to see them to the biggest win in the country's history.
They will go again on Monday, when they take on South Korea, in what is likely to be a de facto knockout game.
Japan will face the Czech Republic on Tuesday, in what is a dead rubber. Shohei Ohtani, who went hitless against Australia for the first time in the tournament, is likely to be rested as their side will rotate for the clash.
Chinese Taipei win classic against South Korea
In Sunday's earlier game in Tokyo, Chinese Taipei took their second-straight victory after beating South Korea 5-4 in extra innings.
After falling to Australia and Japan earlier in the tournament, Chinese Taipei knew they had to beat today's opponents to have any chance of qualification from Pool C.
They came out swinging. Starman Yu Chang homered in the second inning to give them the lead, before South Korea replied, after a quiet start, in the fifth.
Shay Whitcomb, who has been in blistering form for South Korea, grounded into a double play, but it was enough for Min Ahn to score from third.
Their opponents were undeterred, as Tsung-Che Cheng smashed their second homer of the day to put them back in front.
The see-saw battle continued into the sixth as Kim Do-Yeong hit a towering bomb of his own to give South Korea their first lead of the game.
Chances came and went for Chinese Taipei to draw level, but the drama wasn't done as Whitcomb's own home run to score two runs and send his bench into delirium. Do-Yeong silenced that quickly, making it 4-4 with an RBI double as the game headed for extras.
Kun-Yu Chiang bunted the runner in from third to give Chinese Taipei a vital lead in the 10th, and they saw the game out to start huge celebrations and keep themselves alive in the tournament.