The eight-year-old, trained by Gordon Elliott and Davy Condon, went early and held on to the lead, holding off the charge of favourite Dedigout.
The 10-1 shot also condemned Mikael D'Haguenet into third place.
There was delight from the trainers, who had also tasted Cheltenham Festival glory earlier in the month when Flaxen Flare won the Fred WInter.
"[Realt Mor] was good at Navan last time and while it wasn't much of a race that day I suppose only a decent horse wins by 25 lengths," said Elliott.
"He has a fair engine and he showed that today. I'm delighted for the owners. We've had a Cheltenham Festival winner and now a Grade 1 winner in a couple of weeks."
Earlier, Annie Power's unbeaten streak continued when the five-year-old favourite won the Irish Novice Hurdle.
The mare, trained by Willie Mullins and ridden by Ruby Walsh, is now unbeaten in seven races. She was at the rear of the field for much of the race, but sliced through to the front and pulled well clear on the home stretch, eventually winning by a resounding 12 lengths.
Mullins said: "She is what I said she could be, but I still don't know how good she is. She might go for the Grade One (mares hurdle) at Punchestown.
"She's starting to show what she shows at home. She's a good mare and keeps improving. She could be anything. I don't know how much is left in the tank. She did it so easy. Ruby said she idled a bit in front.
"I didn't think two and a half miles would be a problem, but I didn't think it would bring about the improvement she showed. She could easily come back in trip. It looked a slow pace. The faster it got the better she got and the better her jumping got."
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