Nepal survived a last-over scare to score the required 13 runs, with 10 runs coming from the first two deliveries and a last-ball misfield producing the winning runs.
Joining Nepal at the March 16-April 6 tournament in Bangladesh are the United Arab Emirates, who return to the global stage for the first time in 17 years.
The UAE qualified courtesy of successfully defending a modest score of 118 runs to upset the Netherlands by 10 runs.
The last time they competed at this level was at the cricket World Cup in 1996.
Nepal and the UAE join Ireland and Afghanistan, who booked their tickets on Monday, at the finals with the two remaining qualifiers to be determined on Thursday.
Nepal, United Arab Emirates qualify for ICC World Twenty20
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