Chasing 171, Nepal relied on a 74-run opening stand between Kushal Bhurtel and Aasif Sheikh, followed by a crucial 73-run partnership between Dipendra Singh Airee and Gulshan Jha to reach the target with four balls to spare.
Despite a strong bowling performance from Scotland's Michael Leask (3/20), Nepal held their nerve in a match that swung back and forth between the teams.