Andre Ayew headed a second-half winner as West Ham snatched a 2-1 victory at Turf Moor.
Already assured of Premier League survival and their highest finish since 1975, the Clarets were in the mood to celebrate and Sam Vokes enlivened the atmosphere by putting them ahead.
But Sofiane Feghouli responded with a quick leveller and, after Sean Dyche's men wasted several chances to regain the lead, Ayew punished them by pouncing on a rebound after 72 minutes.
It made for a slightly disappointing end to the season for Burnley, who had claimed 10 of their 11 wins at home, but the appreciation of their fans for a fine effort was not diminished.