After a goalless first half, the Solomons took the lead through Gagame Feni, the Telekom S-League's top scorer, in the 68th minute.
The Solomons continued to push forward, and were rewarded with a second goal by Central Coast's William Komasi in the 81st minute.
Vanuatu had started the tournament with an upset 2-1 win against Fiji.
In the day's other match at Churchill Park, the Fiji senior team drew 2-2 with the Fiji Under-20s side.
The senior side finished with ten men when Tevita Warainivalu was dismissed in the second half.
