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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."

Prime Minister David Cameron said last week that money was "no object" in the effort to aid households and businesses flooded in England in recent weeks.
Parts of Dumfries and Galloway were hit by flooding over the festive period.
Councillor Colin Smyth has called on Scottish ministers to ensure the region gets a share of any additional cash.
He said: "What we are asking is, if there is funding being made available in the south of England will Scotland receive some of that as part of the Barnett formula?
"And secondly we want to know from the Scottish government, if this is the case, will they make sure that money is spent in the areas that actually suffered from flooding."
Dumfries and Galloway was one of the Scottish areas hardest hit by flooding at the end of last year and over the new year period, with residents of Kirkconnel, Carsphairn and Moniaive having to be evacuated.
One family was rescued by helicopter after their farm house beside the River Nith near Closeburn was cut off by rising water.
Just days later, coastal communities along the Solway bore the brunt of more severe flooding as high tides, storm surges and gale force winds combined to overwhelm sea defences.
In January, Scotland's Environment Minister Paul Wheelhouse said flood risk management was a "priority".
He said Cosla and the Scottish government had a "pot" of Â£42m available to local authorities to bid for to help tackling flooding issues.

The 25-year-old man, from Wigan, is being held by Greater Manchester Police in connection with attacks on two men.
One, a 25-year-old from Skelmersdale in Lancashire, has been charged with attempting to meet a girl under 16 following grooming.
The other, 19, has been released on bail on suspicion of a similar offence.
Police said the first incident occurred at about 21:00 BST on Friday when the 19-year-old arranged to meet what he believed was a 14-year-old girl in a church car park in Atherton, near Wigan.
On his arrival he was filmed being attacked by a group of men who accused him of being a paedophile.
He escaped but later received messages demanding money and threats the footage would be uploaded to Facebook.
He reported the incident to the police on Saturday, was then arrested and subsequently bailed pending further inquiries.
Later that day, at about 14:40 BST, shoppers at Market Place in Wigan witnessed the Skelmersdale man being assaulted.
He also was accused by a group of arranging online a meeting with a 14-year-old girl. One of the men in the group attacked him, knocking out two of his teeth.
The episode was filmed by the group and has since been posted on the internet.
The man got away and reported the events to the police, who arrested him and charged him with grooming.

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"We looked through pinhole viewers and colanders. We also made a viewer out of a poster tube. We saw the sun turn into a tiny crescent and we got really chilly! It was amazing!"
Kestrels Class, Welford Sibbertoft and Sulby primary school, Northamptonshire
Grosvenor retained the Schools' Cup by beating St Columb's 3-1 after extra-time in the final at Seaview.
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Dumfries and Galloway Council has said flood victims in the area should receive a share of UK government money to help those hit by severe weather.
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A man has been arrested on suspicion of vigilante assaults and blackmail of men alleged to have tried to meet with underage girls, police said.
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Many parts of the UK have experienced a very rare partial solar eclipse, one of the most spectacular in years.