The Omani side – in the competition for the first time since 2011 – were pre-match favourites after winning the first leg 3-1.
But a 10-man Al Shabab claimed a 3-1 win of their own to force a shootout, only to run into the inspired Saham goalkeeper Sulaiman Al Bariki.
Al Bariki made two penalty saves in the shootout to give his side victory, meaning they will face either Al Nasr or Al Nahda in the final.
UAE Pro League side Al Shabab took just 35 minutes to level the aggregate score at 3-3 after strikes from Carlos Villanueva and Esam Dahi.
Saham responded through Mohsin Jahar on the stroke of half-time, but their lead was short-lived, as Dahi bagged a second in the 58th minute.
The eventual winners should have wrapped up the contest in the second minute of injury time, only to miss a penalty, but Al Bariki was their hero in the shootout.
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