Husain Norchaev scored twice to give visiting Nasaf a two-goal lead at halftime but the Saudis struck twice in three second-half minutes to pull level on Monday night (Tuesday AEST).
Goals from former Leicester and Manchester City winger Riyad Mahrez four minutes into added time and Mohammed Sulaiman 11 minutes later save the home side.
"Everybody had to give 100 per cent in the second half, we had to do more and attack the box to score goals and we did it," said recent French signing Enzo Millot, who scored Al-Ahli's first two goals.
The win earned Al-Ahli an opening three points in the western league phase, in which the 12 teams play eight matches and the top eight finishers will advance to March's knockout rounds.
Saudi Pro League champions Al-Ittihad slipped to a 2-1 defeat by Al-Wahda from the United Arab Emirates with defender Lucas Pimenta scoring the winner deep into added time.
Dutchman Steven Berwijn had given Laurent Blanc's side the lead in the 21st minute.
Caio Canedo levelled from close range in the 62nd minute and, deep into added time, Pimenta pounced after Pedrag Rajkovic blocked Ala Zouhir's header.
Elsewhere, Sharjah of the UAE also picked up a win with two added-time goals against 10-man Al-Gharafa of Qatar earning a 4-3 victory for last season's Asian Champions League Two winners, while Qatar's Al-Sadd fought back to draw 1-1 with Iraq's Al-Shorta in Baghdad.
The opening fixtures in the East kick-off on Tuesday night with Australia's Melbourne City hosting Sanfrecce Hiroshima of Japan.
With AAP.
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