Yu Hai struck the decisive goal in Brisbane with a deflected free-kick after 81 minutes, after Saudi Arabia striker Naif Hazazi had missed a penalty on the hour.
The victory gives China a great opportunity to qualify from Group B, and Perrin was delighted with the determination shown by his players.
"The match was very difficult for us but now we can be very pleased with our performance," he said. "We are very happy.
"Preparation has been very difficult and we have practiced for a very long time but today our tactics paid off.
"We counter-attacked very well, causing many problems for Saudi Arabia.
"I am satisfied with our defensive efforts. We were placed under pressure by the Saudi team but we kept a clean sheet so I am very satisfied."
China face Uzbekistan – who beat North Korea 1-0 on Saturday – in their next match on Wednesday in Brisbane.
