In a first innings reduced to 47 overs, Scotland blasted their way to 321-6, with opener Finlay McCreath top-scoring on 77.
There were also half-centuries for Brandon McMullen (55) and Matthew Cross (58), who both scored quickly in Kirtipur.
Mark Watt and Michael Leask also contributed with impressive cameos down the order, as Scotland significantly improved on their total of 243-8 made in Tuesday's narrow victory over Nepal.
In reply, Brad Currie struck early to remove Shayan Jahangir, but Smit Patel batted fluently on his way to 72 as the United States passed 100 inside 16 overs.
When heavy rain descended, they had reached 160-4 from 26.4 overs, with a daunting revised target of 248 from 32 overs subsequently set.
Number four Saiteja Mukkamalla - on 56 from 59 balls before the rain - launched an astonishing assault upon the restart, reaching his hundred from just 72 deliveries.
It was a knock that ensured the match would go to the wire, but he was unable to close the game out.
With 16 required off the final over, Mukkamalla skied a wide delivery from Brandon McMullen and Scotland captain Richie Berrington took a brilliant diving catch running backwards from extra cover.
Still, USA took nine runs to leave six needed off the final ball for a tied match.
Mohammad Mohsin only managed four, meaning the Scots leapfrog USA at the top of the standings having played five matches more.
"It was a pretty important moment, so I'm luck it stuck in my hands," Berrington said of his catch to remove Mukkamalla.
"That was a fantastic knock and once again we've gone down to the wire. We made it tougher than we would have liked but really important that we held our nerve.
"It took us a while to get going again after the rain break. I'm just pleased we managed to close it out. We're finding a way to get over the line."
