Yuki Soma's first-half goal secured the tournament debutants a place in Saturday's final against defending champions Al-Ahli of Saudi Arabia, also in Jeddah.
Al-Ahli thought they had forced extra time only for the goal to be controversially ruled out by Australian referee Shaun Evans.
Former Newcastle Jets striker Yengi is hoping to become the first Australian to earn a winners' medal in the competition since the Western Sydney Wanderers won it in 2014.
Only former U17 international Alex Grant, who was on the losing side with South Korea's Pohang Steelers in 2021, has played in the final since.
Yengi's progress has richly rewarded the decision to go on loan to Japan from struggling Scottish club Livingston in January and he played a part in Soma's 12th minute goal.
Yengi, the 25-year-old from Adelaide and younger brother of Socceroos striker Kusini, led the press as Shabab attempted to play out, forcing a poor pass from Breno that put defender Bogdan Planic under pressure. Soma robbed him and scored past goalkeeper Hamad Al-Meqbaali.
Al-Meqbaali prevented Erik from doubling Machida's lead three minutes later with a diving save to his left while Shabab Al-Ahli's Kauan Santos hit the crossbar at the other end with 10 minutes remaining in the half.
Zelvia, from the Tokyo suburb of Machida, were fortunate when a 92nd-minute Al-Ahli equaliser was controversially ruled out.
Guilherme Bala appeared to have forced extra time with a stunning long-range strike, but the goal was disallowed after a lengthy VAR review because Al-Ahli restarted play with a throw-in before Machida had completed a double substitution.
"There was a goal that was scored and then it was cancelled, this is a very technical mistake by the referee," said Shabab Al-Ahli coach Paulo Sousa.
"Unfortunately this is what is turning football into rubble. It was a big mistake to choose this referee for this match. We deserved to be in the final and we deserve to play this important game."
Evans had earlier reversed a decision to award Soma a penalty after consulting the pitchside monitor.
On Monday, Al-Ahli beat Vissel Kobe 2-1 and are seeking to be the first team since 2005 to win back-to-back titles in the continent's premier club competition.
With agencies.
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