After losing the first-leg in Tashkent 5-4, the hosts needed to win at the Hong Kong Stadium if they were to progress and they made the perfect start after just two minutes.
Lee Chi Ho whipped in a cross from the right and Leandro rose unmarked to head onto the inside of the post and into the back of the net.
The hosts continued to dominate with Leandro causing all sorts of problems for the Neftchi defenders, and he almost grabbed his and South China’s second after seven minutes.
The former Atletico-MG forward charged towards goal before drilling a shot that goalkeeper Yuriy Tsoy could only punch back into the path of the 24-year-old, who then compounded to send his second effort wide with the goal at his mercy.
Leandro again tested Tsoy in the 14th minute when the goalkeeper had to be alert to parry a powerful shot away for a corner.
Neftchi, meanwhile, were looking lethargic in comparison and failed to create a chance of note in the first half.
They finally had an effort on goal two minutes after the restart when they were awarded a free-kick 25 yards from goal but Anvar Berdiev could only send the ball over the bar.
Leandro was the architect of South China’s next chance when he sprayed a pass across the pitch for the unmarked Lee and the defender took one touch before striking an effort high and wide.
The hosts continued to press for a second that would effectively end the game as a contest as Chan Wai Ho’s glancing header was cleared off the line by a defender before substitute Bai He fired wide.
But Neftchi should have equalised in the 70th minute when a mistake by Ramon Rodrigo put the hosts on a two-on-two attack.
Bahtiyorjon Yakubov then sent Alisher Halikov clear but South China goalkeeper Zhang Chunhui made himself big before palming away the striker’s point-blank shot.
Zhang was again on hand to punch away a dangerous looking free-kick from Iqboljon Akramov as South China successfully defended their slender advantage to book their place in the last four.