The Iranians went through on the away goals rule after winning the first-leg 1-0.
Padovani scored the opener for Naft Tehran and Omar Al Soma scored a brace for the home side.
In the 32nd minute Naft opened the scoring when Iman Mobali's free-kick from the right flew over the Ahli defence and Padovani was there to shoot past Abdullah Al Muaiouf.
Two minutes later Ahli nearly scored when Salman Muwashar's shot went narrowly over the bar.
Then in the 36th minute the home side equalised when Soma scored from close-range after receiving a decent pass from Aqeel Al Sahabi to make the score 1-1.
With three minutes remaining in the half, the Saudis went ahead when Soma struck again, this time with a header from Salman Muwashar's cross leaving keeper Alireza Beiranvand well beaten.
In the second half Naft played well and in the 51st minute nearly scored when a header by Vahid Amiry hit the post.
Eleven minutes from time, Soma was denied a spectacular third goal when his long-range free-kick hit the woodwork.
Ahli grew increasingly desperate and came close late in the game when Al Shabi was denied when his header was saved by the keeper.
In the end Ahli could not get the vital goal to stop Naft from advancing.