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The Swans shot into the lead in the 29th minute when Bersant Celina connected home a through ball from Andre Ayew.
Before Jordan Hugill in the 66th minute put the visitors on level pegging.
But Swansea City restored their lead four minutes later through in-form Borja Baston from 12 yards.
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And Andre Ayew popped up again to create the goal that put the game beyond the reach of Queens Park Rangers- the former West Ham United forward's incisive cross was headed home by Sam Surridge.
Andre Ayew seems to have rediscovered his form- he scored twice in the League Cup for Swansea City last week.
Andre captained the Black Stars in the 2019 Africa Cup of Nations staged in Egypt in June-July.