The Flames, who drop to the bottom of Group L with two points from four games, were hoping for a better showing at home having held the Syli Nationale to barren draw in the reverse last Friday in Conakry.
Despite going in front through Chiukepo Msowoya's 30th minute goal, the visitors fought their back into the game.
Lamine Yattara nodded in the equalizer in added time of the first half before Idrissa Sylla added the second after 59 minutes.
Guinea has five points, same as Swaziland, three shy of leaders Zimbabwe.
Meanwhile, Guinea Assistant Coach Hatton Lauren believes his charges are back in contention for a place after grabbing their first win of the campaign.
“We came here to fight and we got the result. Playing two games within a few days was not easy, but we fought back after conceding early. Our players were not used to playing on such a pitch, but in the end we prevailed,” he added.