Naft, who defeated Bahrain’s Al-Muharraq in its opening Pool A match on Tuesday, beat Fubon Braves of Chinese Taipei 68-66.
Hamed Haddadi led the Iranian team with 18 points and Shao Chieh Kuo had 19 points for Fubon.
Naft will face Thailand’s Hi-Tech Bangkok City on Thursday.
Pool B consists of China’s Guangdong Southern Tigers, Ulsan Hyundai Mobis Phoebus from South Korea, Japan’s Alvark Tokyo and Al Riyadi Beirut from Lebanon.
The 2019 FIBA Asia Champions Cup is the 28th staging of the FIBA Asia Champions Cup, the international basketball club tournament of FIBA Asia.
The competition is being held in Thailand from September 24 to 29.