Justin (60) and Anthony (62) became the first brothers to score half-centuries in the same T20 World Cup match, as Italy, a country without a single natural cricket pitch, chased down a target of 124 with 44 balls to spare.
Italy's decision to bowl first in Mumbai paid off when their spinners shut down Nepal's attempts to get a partnership going, with Crishan Kalugamage (3-18) and Benjamin Manenti (2-9) getting wickets at regular intervals.
Player of the match Kalugamage dismissed Nepal captain Rohit Paudel (23) and helped restrict Nepal to a meagre total of 123.
The Italian openers, undeterred by the absence of their captain Wayne Madsen, who dislocated his shoulder during Monday's loss to Scotland, started aggressively with Justin Mosca hitting three sixes and three boundaries to help his team reach 50-0 in four overs.
He reached 50 off 37 balls in the 11th over, and Anthony hit a six in the next delivery to reach his own half-century.
Anthony scored the winning run with a shot towards cover, getting Italy to 124-0 in 12.4 overs, as his teammates rushed onto the field to celebrate their milestone victory.
"I always wanted to help the team win and do my best for my nation Italy... it's a massive moment for me after a lot of sacrifices," said Kalugamage, a Sri Lankan-born pizza baker, as his voice shook during the post-match presentation.
Italy next face former champions England in Kolkata on Monday.