The Ghanaian striker, who was signed from Aston Villa on deadline day in January, had gone 13 matches without a goal until Sunday when he rose to the occasion to put is trailing side back into the game.
Jonny Evans put the Baggies in the lead with a free header on 33 minutes to hush the crowd inside the Liberty Stadium and the visitors went into the half time break confident of a victory.
Then Ayew stepped up the pressure with his own header, getting onto the end of Fernando Llorente’s header inside the box to put it past goalkeeper Ben Foster on 72 minutes.
Sensing the enormity of the occasion, the 25-year-old sank to his knees with hands pointed to the skies in appreciation at finally breaking his duck.
Llorente would pop up with the winner on 82 minutes to cement the win for the Swans as they ended the season in 15th spot after several weeks of struggling in relegation waters.
Even though Jordan did not enjoy the same kind of first season that his older sibling Andre had at Swansea, he has become one of the trusted men for manager Paul Clement.
He grabbed three assists in 14 appearances, nine of which he started. He would hope to have a great pre-season with the squad that should give him a better head start when the new season resumes in August.