The spinners came to the fore on a slow, turning track in St Vincent and for much of the game it seemed that the Nepal bowlers would be the match-winners.
They kept a powerful South Africa batting unit under control throughout with wrist-spinner Kushal Bhurtel (4-19) the standout and Dipendra Singh Airee taking 3-21 with his off-breaks.
Reeza Hendricks top-scored with 43 but with the Nepal bowlers on top, it took a cameo from Tristan Stubbs (27* off 18 balls) to give the Proteas an ultimately vital late boost.
“You have to give Nepal a lot of credit, throughout the game they put us under a lot of pressure and it shows the quality they have,” said South Africa captain Aiden Markram.
Nepal began their chase well, got through the powerplay unscathed and even when Shamsi claimed two wickets in the eighth over, they calmly pressed on.
A 50-run stand between Aasif Sheikh and Anil Sah was broken by Markram in the 14th over but with just 30 more needed, Nepal remained on track for victory.
But when Shamsi had Singh Airee caught behind down the leg side before bowling Aasif for 42 to leave Nepal 100-5, the nerves set in.
Nepal still whittled it down to eight to win from the last over, seven for the super over, and that became two from two balls.
Baartman came through for South Africa, though, and they clung on for the narrowest of victories.
“Definitely relieved,” said Shamsi. “The team is standing up to the pressure and that’s great to see.”
Nepal captain Rohit Paudel added: “I’m very proud of the unit, the way we bowled and batted.
“We were very close but a little far.”
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