The former Asante Kotoko player scored late in the game to end Trelleborgs losing streak in the league.
The home side took the lead through Oscar Johansson in the 51st minute but Brage leveled two minutes later after Bjarni Mark Antonsson.
Brage then took the lead in the 67th minute from the spot through Christian Kouakou.
With the game headed for a defeat, Trelleborgs then pulled parity after Ghanaian forward Fatawu Safiu scored at the death of the match.
Safiu has now scored twice in six games for the Superettan side.