Abdulaziz al Miqbali and Cisse Ely scored on either side of the break for Fanja, while Javad Nekonam reduced the margin for the visiting side.
Both teams kept a tight defence in the first half an hour with no shots taken on target. Fanja skipper Ahmed Hadeed received a yellow card in the 38th minute for diving.
The first goal came in the 42nd minute when a long pass was received by Fanja’s Mohammed al Mashari, whose feeble shot failed to make it to the goal. However, an alert Miqbali was quick enough to nudge it into the net for the breakthrough.
No other chances were created in the first half.
The second half began slowly, but in the 52nd minute, Yemeni referee Mukhtar Saleh al Yarimi pointed to Kuwait's penalty spot after Fanja's Raeed Ibrahim was fouled inside the rival penalty area. Ely converted from the spot in style, placing the ball into the top left corner.
Kuwait SC reduced the margin in the 65th minute when Nekonam headed in off a corner-kick from Waleed Aly Jomah.
Five minutes later, Fanja was reduced to ten men when captain Hadeed collected his second yellow card of the night for showing dissent following an altercation with referee.
Looking to make the most of the numerical advantage over a 20-minute period, the visitors attacked more in search of the equaliser. But they were denied by a spirited Fanja defence.
Fanja coach Hicham Jadrane said after the win, “This match was very difficult as it was against the best team in the tournament. We didn’t allow them any chances.”
Kuwait SC coach Marin Ion said both the teams deserve to progress to the next round. “It should have been a draw today. But in football, any minute a game can change. It was a nice match as both the teams played good football,” he said.
In another AFC Cup game, Oman's domestic league champion Suwaiq suffered a 0-1 defeat at the hands of Jordan’s That Ras in a Group A game at the Amman International Stadium.