Norimoto, who went 14-10 with a 3.02 ERA this season for the Rakuten Eagles, struck out six over five perfect innings.
Cano was hit by a pitch on the right foot in the seventh inning. The Mariners confirmed later Saturday that X-rays revealed a fracture in his small toe and he is expected to miss 3-4 weeks.
Hayato Sakamoto and Sho Nakata each hit a two-run homer as Japan took a 3-0 lead in the five-game series.
"It's too good to be true," Norimoto said. "I wanted to see how my pitches would work against MLB hitters. The fact that my teammate (Motohiro) Shima was catching made me feel at ease and I was able to perform as usual. The atmosphere at the park was really nice. It was the best outing of my career."
Yuki Nishi took over from Norimoto and struck out four with one walk over two innings. Kazuhisa Makita struck out two in the eighth and Yuji Nishino retired the side in the ninth.
"The story tonight was in the hit column with a zero on it," MLB manager John Farrell said. "Norimoto was outstanding. He was very efficient. He has a powerful fastball and very good late action to go with his split, his slider and cutter."
Sakamoto connected off MLB starter Jeremy Guthrie in the second inning, and Nakata made it 4-0 in the third with a blast off Guthrie over the left field wall.
Guthrie took the loss after giving up four runs on five hits in five innings.
The MLB All-Stars won an exhibition game 8-7 before the start of the series but have scored just four runs over the first three games.
Chris Capuano will pitch Game 4 while Shintaro Fujinami will take the mound for Japan.
"We will visit with our coaching staff and try to come up with a lineup that has the ability to go up against Fujinami, who we know is a very good pitcher," Farrell said.