The Saudi Arabian club trailed 2-1 after 34 minutes but also got goals from Ahmed Hadid, Luciano Leguizamon and Amine Chermiti to move within touching distance of the final.
The second leg will be played in Tokyo on October 28, with the winner facing either Qatar's Umm Salal or Pohang Steelers of South Korea. Pohang won the first leg 2-0 at home Wednesday.
Nagoya Grampus played with 10 men for most of the match after defender Akira Takeuchi was red carded in the sixth minute for a harsh challenge.
However, it was the Japanese visitors who went ahead in the 15th minute when Joshua Kennedy rose up to head the ball from close range, giving Al Ittihad goalkeeper Mabrouk Zayed no chance.
Al Ittihad equalised in the 25th through Hadid, who collected the ball inside the penalty area and fired into the back of the net.
The Saudis again showed some weaknesses in defense and conceded a second goal nine minutes later when Nakamura was given time and space to regain his side's lead from just six yards.
But Noor scored three times in a 15-minute span in the second half, while Argentine striker Leguizamon and Tunisia's Chermiti hit one each in the closing stages to give Nagoya Grampus's a tough task in the second leg.
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