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Conor Kernohan put the holders ahead with a close-range header from Stuart Nelson's cross in the second half.
But Matty Doherty quickly levelled for the Derry side with a penalty after Grosvenor keeper Tim Larmour had brought down Joe McCartie.
In extra-time Josh Kelly rounded keeper Gareth Muldoon to make it 2-1 and skipper Nelson's low shot sealed it.
Nelson, who also played in Grosvenor's 2016 triumph, praised the effort of losing finalists St Columb's.
"They are a quality side and, as you could see today, they stroke the ball about nicely," said the winning captain.
"I thought our fitness maybe told in the end, although we got lucky with two breakaway goals.
"We had to dig deep, but the boys have been brilliant all year."
Grosvenor retained the Schools' Cup by beating St Columb's 3-1 after extra-time in the final at Seaview.