The hosts had gone in front in the 38th minute when Ilkhom Shomurodov found the back of the net but a 15-minute period in the second-half ultimately cost them the points.
Alexander Andic’s free-kick levelled the contest just after the hour mark before Al Suleiman struck with 12 minutes to go to seal a crucial victory for Kazma and maintain their 100% record as they eye a place in the knockout stage.
Nasaf began the game on the offensive and created a number of chances, the best of which fell to Samandar Shodmonov but the young midfielder was unable to convert with just keeper Ahmed Al Fadhli to beat.
Kamoliddin Murzoev then sent a header wide of the target before Nasaf took the lead seven minutes before the break.
Hamza Karimov delivered a cross from the left flank that found Shomurodov in the area and the striker made no mistake to score his fourth goal of the tournament.
Nasaf looked well equipped to defend their slender advantage in the second period but the game was turned on its head during a quarter of an hour spell.
Andic hit a powerful free-kick in the 63rd minute that beat keeper Dmitry Kozachenko and levelled the encounter.
Then in the 78th minute, Suleiman somehow managed to beat Kozachenko and find the back of the net despite the attentions of no less than five Nasaf defenders.
The Uzbek side tried in vain to hit back but shots from Siarhey Krot, Artyom Filiposyan and Rustam Kadyrov all failed to breach the Kazma rearguard as the equaliser they were desperately searching for failed to materialise.
The result means that Kuwaitis Kazma now top the group on nine points with Nasaf second having collected six from three games.
The two sides will renew acquaintances on April 7 at the Friendship and Peace Stadium in Kuwait.