The result left St. Lucia atop Group 2 with six points, three better than St. Vincent and Guyana, which beat Curacao 2-1 in the first game of Tuesday's doubleheader.
Two teams will advance to the second round. Thursday's group finale will see St. Vincent face winless and already eliminated Curacao, and St. Lucia against Guyana.
Paul, who had the first goal in St. Lucia's 5-1 victory over Curacao on Sunday, had the lone strike in the 69th on Tuesday. The goals in St. Lucia's last two matches contrast with its previous run, in which it went winless in six games, and scored only one goal in its previous four games.
In the earlier game, Gregory Richardson converted a penalty for a second consecutive game to give Guyana the victory.
Vurnon Mills put Guyana ahead within 60 seconds after kickoff and Richardson doubled the lead three minutes before halftime.
Guyana damaged its own cause when Colin Nelson put a ball in his own net in the 53rd, but Curacao couldn't must much more and then had striker Quinston Bartholomeus ejected in the 89th.