Hughton Hector also scored for Trinidad, which bounced back from a surprising 2-1 loss to Bermuda on Friday.
Peltier, who entered with only one international goal, got off to a fast start and kept pressuring Barbados. The 23-year-old scored in the seventh minute, then added two more in the second half at Hasely Crawford Stadium.
Hector finished the scoring in the 88th minute, taking advantage of a defensive error by Barbados.
With one qualifying spot available, the Soca Warriors are competing with Guyana for the lead in Group B.