Stand-in Arsenal goalkeeper Kepa Arrizabalaga gifted City their first goal when he fumbled Rayan Cherki's cross on the hour mark, with O'Reilly on hand to head home from close range.
A rampant City then doubled their advantage just four minutes later after O'Reilly converted a cross from Matheus Nunes to send Pep Guardiola dancing in delight along the touchline.
Riccardo Calafiori hit a post and Gabriel Jesus struck the crossbar as Arsenal went in search of a response, but City saw out the victory as Guardiola landed the 19th trophy of his amazing 10-season City tenure.
"(It's an) unbelievable feeling to win a final and to beat this team," O'Reilly told Sky Sports.
"We know how good they are. We need to build on it now, it'll give us momentum."
Mikel Arteta's Arsenal had headed into Sunday's final hoping to finish the season with an unprecedented four trophies, as well as ending their six-year wait for silverware.
But the damaging defeat at Wembley Stadium will do little to ease their tag as the 'nearly men' and also raise significant questions over the remainder of their campaign.
City are nine points behind the Gunners in the race for the Premier League title but they have a game in hand on Arteta's side, who also have to travel to the Etihad Stadium next month.
Arteta will have been intent on silencing the doubters to claim just the second trophy of his tenure and his first in nearly six years.
But the Spaniard was served a sobering lesson by his one-time mentor Guardiola.
"I'm very sad. It is a very hard one to take, especially for our players and our supporters because we know how much it means to them and how much we want that," Arteta said.
"We will manage that energy in the right way and we have to go through that pain and disappointment. It's normal and it's part of football."
Both Arteta and Guardiola elected to place faith in their back-up goalkeepers, but while James Trafford produced a fine triple save, first from Kai Havertz and then two follow-up efforts from Bukayo Saka, after just seven minutes, Kepa would end up taking centre stage for all the wrong reasons.
On the hour mark, Kepa, who has not played in the Premier League at all this season, dropped Cherki's dinked cross and O'Reilly headed in from on the line.
Only four minutes later O'Reilly struck again, this time with a header that Kepa could do nothing about.
With AP.
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