The goals took Ameobi’s tally for the season to five with nine assist in 43 league appearances.
The last time the former Newcastle United forward scored was in February.
The 28-year-old younger sibling to former Super Eagles striker Shola, was replaced with 14 minutes left in the game.
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Swansea took the lead in the eight minute by Rhian Brewster before Ameobi equalised on 20 minutes.
The visitors took the lead again this time through Ghana international Andre Ayew from the penalty spot on the stroke of half-time.
But 10 minutes into the second half Ameobi got on the score sheet again to make it 2-2.
Nottingham Forest were handed a lifeline after Kyle Naughton was shown a straight red card in the 82nd minute.
Despite the numerical advantage, Nottingham could not find the winner and had to settle for a share of the spoils.
Wednesday’s result means Nottingham are in fifth position on 70 points and occupy one of the four promotion play-off spots.
The three other teams in the play-off spot are Brentford, Fulham and Cardiff who are third, fourth and six respectively.
By James Agberebi
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