The result marks another setback in the Black Star’s World Cup preparations under Carlos Queiroz, with three defeats and one draw in their last four outings.
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Wales dominated large spells of the first half, with Daniel James twice going close as he hit both the post and crossbar in quick succession.
After a quiet opening hour, the West Africans eventually took the lead when substitute Caleb Yirenkyi reacted quickest to score from a rebound.
However, Wales pushed for a response and were rewarded in the 93rd minute when Neco Williams delivered a cross from the right and Koumas headed home his first international goal.
The draw also means Wales remain without a win in three matches under Craig Bellamy, despite encouraging signs in performance.