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The win has sent them to the summit of the English Championship table, which is a point clear of Leeds United.
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The forward's 65th-minute strike sealed a comeback win for the Swans after Charlton had gone ahead inside two minutes through Jonathan Leko, who drove home from 15 yards with the aid of a deflection.
Yan Dhanda levelled for Swansea with another deflected effort at the end of a bright passing move, before Ayew's close-range effort secured a sixth victory in 10 league games under Cooper.
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Charlton could have few complaints as they failed to build on their impressive weekend win over Leeds United.
The match-winner is Andre Ayew’s first league goal since May 2016.