Siarhei Krot opened the scoring for the visitors in the 33rd minute before adding a second goal a minute after the break.
Nasaf scored a third after 54 minute through Ilkhom Shomurodov, who then capped the victory with his second and his side’s fourth just after the hour mark.
It had been the hosts that had enjoyed the majority of possession in the opening exchanges and they carved out the first chance after 13 minutes when Hassan Maatouk fired just wide.
Four minutes later and Al Ahed threatened again as Hamzeh Salameh broke into the area before unleashing a powerful drive that fizzed past the left upright.
There followed a lull in proceedings before Al Ahed produced their next chance on the half hour when Mahmoud El Ali’s neat pass found Maatouk but his shot was straight at Nasaf goalkeeper Dmytro Kozachenko.
The Lebanese side paid for their profligacy as Nasaf opened the scoring three minutes later when Hamza Karimov ran down the left before crossing into the area for Krot, who headed beyond goalkeeper Mohamad Hammoud and into the net.
Buoyed by that goal Nasaf went in search of a second to kill the game off and they found it in the first minute of the second half when Krot turned home Karimov’s cross.
The Uzbeks were now in the ascendancy and nearly added a third in the 49th minute when Samandar Shodmonov found space inside the area and fired a powerful shot that went just wide of the right upright.
But another goal duly arrived five minutes later when Botir Karave looped a ball to Shomurodov, who then sent a header into the back of the net.
The hosts almost reduced the deficit on two occasions soon after but Salameh and Maatouk failed to make their opportunities count and the chances past.
Instead it was Nasaf who added a fourth goal in the 66th minute when Krot played a pass to Shomurodov and the forward made no mistake from a close range to round off the win.