Earlier, Costa Rica had taken a 1-0 lead on Walter Centeno's goal in the 62nd minute.
Boucicaut responded to Centeno's goal with a blast from 15m which beat Costa Rica goalkeeper Jose Francisco Porras.
Costa Rica, who needed three points to move up in the Group A standings after a 2-1 loss against Costa Rica on Wednesday, applied repeated pressure early in the second half but were denied by diving saves from Haiti goalkeeper Gabart Fenelon.
Fenelon twice dove to stop shots from Michael Barrentos in the 51st and 52nd minutes.
Guadeloupe leads the group with four points.
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