The Cullentra handler has been the dominant force in staying handicap chases in Ireland in recent years, but this €100,000 contest had previously eluded him.
He saddled no less than six runners in this year's renewal and Monbeg Notorious was the 7-2 favourite in the hands of Jack Kennedy.
Visored for the first time after winning a beginners' chase at Punchestown on New Year's Eve, the Gigginstown House Stud-owned seven-year-old made steady progress to track Fine Theatre into the home straight and took over jumping the third fence from the finish.
Monbeg Notorious soon drew clear and safely negotiated the remaining obstacles to seal an impressive 11-length success.
The result further increases Elliott's already significant lead over Willie Mullins in the race to be crowned this season's champion National Hunt trainer.
Elliott was only narrowly denied a one-two, with Noel Meade's Wounded Warrior beating the winner's stablemate Space Cadet to the runner-up spot by a head.
Kennedy said: "He never missed a beat the whole way. He jumped and travelled and I was probably left in front a bit soon, but he dug deep and kept galloping.
"All he does is stay really, but today I was quite surprised by how well he travelled. Today was definitely his day.
"Any other 18-year-old would kill to be in the position I'm in. I'm very lucky."
Elliott said: "It's great when it works out. It's great for Jack, for me, Gigginstown and for the horse. I think we've won nearly all the big staying chases in Ireland now.
"It was his first run in handicap, so it was a bit of a worry, but it's worked out great. Everyone is happy.
"He's a big galloper. He's won a Thyestes Chase now and whatever happens now will be a bonus.
"He's a bit of a character at home and doesn't do anything too fancy, but he loves that soft ground and jumped and galloped them into the ground.
"In beginners' chases he's been having to do his own donkey work and he's lairy in front. Today he had something to aim at and it worked out great."
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