Kaiyne Woolery had brought Sligo level before half-time, but Shelbourne scored four unanswered goals after the break.
Sligo Rovers have been relegated from the League of Ireland Premier Division following a 5-1 defeat to Shelbourne at Tolka Park.
The result brings an end to Sligo's 22-season stay in the top flight, with the club set to compete in the First Division in 2027.
Kaiyne Woolery had brought Sligo level before half-time, but Shelbourne scored four unanswered goals after the break.
John Martin scored twice for the Dublin side, with Daniel Kelly, Ademipo Odubeko and Milan Mbang also on target.
The victory moves Shelbourne into fourth place, two points ahead of Derry City, who have a game in hand.

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