The Omani side are playing in the competition for the first time since 2011 and they continued their impressive group form when Mohsen Essence put them in front after 11 minutes at Sultan Qaboos Sports Complex on Monday.
Saham doubled their lead six minutes into the second half, with striker Mohamed Al-Zeno this time on target to leave the visitors up against it.
Rashid Hassan halved the deficit just after the hour-mark, but they were unable to maintain the pressure and Saham extended their lead late on.
With a minute of normal time to play, Fahd Aljelbobe gave the home side some breathing space ahead of the second leg at Maktoum bin Rashid Stadium next Tuesday.
For two-times champions Al Shabab have it all to do as they attempt to reach the final for the first time since they lifted the trophy in 2011.
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