The two sides went into the second leg in Riyadh with the tie delicately poised, having played out a 1-1 draw in August.
And after a pulsating return fixture, it was a goal from Naoya Kondo that proved to be the difference, as his second-half header sent the Japanese through.
Al Shabab struck the first blow, with Naif Hazazi edging them ahead after 10 minutes with a powerful header from Macnelly Toress' corner.
However, their celebrations were cut short when Reysol levelled just three minutes later.
Tae-Hwi Kwak gifted the visitors a way back into the tie when he turned the ball past his own goalkeeper from close range to level the scores.
And Reysol put on foot in the last four when Kondo edged them ahead, heading in the crucial away goal after 73 minutes.
With time running out Hassan Fallatah levelled on the night, but it was not enough as the Reysol became the first Japanese club to reach the semi-finals since 2009.
They will face China's Guangzhou Evergrande in the last four.
