Evans had headed Darren Fletcher's corner past Kristoffer Nordfeldt at the back past in the 33rd minute to give the visitors the lead, but Ayew nodded the hosts level in the 72nd minute as Swansea extended their undefeated run to five games.
West Bromwich finish in 10th on 45 points, missing the opportunity to equal their best top flight finish since 1981.
(Reporting by Ed Dove)
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