The Omani side - in the competition for the first time since 2011 - are in a strong position thanks to goals from Mohsen Essence and Mohamed Al-Zeno.
Although UAE Pro League side Al Shabab pulled one back through Rashid Hassan, Saham restored their two-goal advantage in the final minute with a Fahd Aljelbobe strike that puts them in control for Tuesday's return encounter.
Saham go into the game in fine form, having lost just once in their last 11 games in all competitions - and they have not tasted defeat by two goals or more since February.
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