Luton Shelton converted a penalty in each half for Jamaica, which lost on a tiebreaker to Mexico for second place in their World Cup qualifying group and was eliminated.
"After the disappointment of the World Cup, we needed this and we did it," Barnes said. "We got a bit sloppy in the second half, but overall I'm happy."
Jamaica, Grenada, Cuba and Guadeloupe qualified for next year's Gold Cup.
Guadeloupe won the third-place game on penalties, 5-4, over Cuba after the match was ended in a 0-0 tie.
Dec. 15 in Kingston
Jamaica 2 Grenada 0. Goals: Shelton pen. 15, pen. 73.
Jamaica -- Ricketts, Thomas, T.Marshall, Phillips, Austin, Morrison, Thompson, Richards (Cummings, 75), Vernan, A.Williams (Dean, 65), Shelton (Moodie, 87).
Grenada -- Noel, Phillip, Langaigne, M.Marshall, Modeste, Leo, Julien (F.Williams, 77), Baptiste, (J. Williams, 83), Rennie, Charles, Bain.
Referee: Neal Brizan (Trinidad & Tobago).