The 10-year-old, a faller in the last two runnings of the Aintree showpiece, was sent off the 11-8 favourite after winning the Thyestes Chase and led just about all the way in the Grade Two contest.
Mount Benbulben, who was conceding 7lb, made a brave attempt to throw down a serious challenge but was never jumping particularly well and the Ruby Walsh-ridden On His Own stamped his authority between the final two fences before scoring by 12 lengths.
Mullins said of the Graham Wylie-owned winner: “He’s a natural jumper, coming off a hard race in the Thyestes I thought that was a magnificent performance.
“After that we might have to rethink about Aintree, I was quite keen after the Thyestes but now we might look at the Bibby Gold Cup at Punchestown.
“We’ll have a chat with Mr Wylie, I think he’s after taking a jump in grade after that. I was thinking that in the stands and funnily enough that was the first thing Ruby said to me when he came back in.
“He’s just going out of handicaps and could win a really good race.”
Mullins had started the day in fine heart as Abbyssial made all to lead home a one-two for the yard in the Winning Fair Juvenile Hurdle.
Paul Townend’s mount jumped well in the main in the colours made famous by Florida Pearl, and the only danger going to two out was his Walsh on his stablemate Adriana Des Mottes.
Asserting between the last two flights, the 11-4 second-favourite swished his tail a couple of times in holding the renewed challenge of the 8-11 market leader, but was always doing enough to secure Grade Two honours by half a length.
Mullins said of the French import, who is Irish-bred: “It was a very good performance. I wasn’t happy with his jumping over the first few but other than that he was impressive – when he needed the jumps he got them. He looks to be improving all the time.
“I’ll have to talk to the owner and see if he travels (to Cheltenham) or we keep him at home. I would like a wet Cheltenham for him, he wouldn’t want it to dry and if it did he wouldn’t go.
“He’s one that will go back to France for a race there, but I was saying to the owner earlier that we might skip Cheltenham and go to France but that performance brings Cheltenham back into it.”
A swift double for Mullins, and compensation for Walsh, came when Beluckyagain rewarded favourite-backers in the www.fairyhouse.ie For Special Offers Mares Maiden Hurdle.
The 8-13 chance had a bit to do turning in and was still a length or so down on Ellie Mia going to the final flight, but jumped it well and came home strongly from the running-on Circe’s Island.
And the Mullins day was complete when Westhorpe (13-8 favourite) claimed the bumper under his son, Patrick.
Warne repeated last year’s success in the John McCarthy Memorial Hunters Chase.
Disputing matters from very early on with Seabass, the Brian Hamilton-trained winner (3-1) as given a fine ride by Declan Lavery, who judged matters to perfection.
Seabass ran a cracking race to be second under Katie Walsh, with star hunter Tammys Hill (5-4 favourite) far from disgraced in third in a race not run to suit.
Ted Walsh was thrilled with Seabass, who could have another crack at Aintree and the National, in which he was third to Neptune Collonges in 2012.
Walsh said: “He ran well, I thought he was going to be third so I’m happy he split the two horses. He never runs a bad race, if he’s fit and healthy we’ll give him another run in two or three weeks’ time.
“He can’t run in the hunter chases at Cheltenham or Liverpool.
“He was very sick with a touch of colic at the end of November, so he was six weeks behind . I’m delighted with him, he showed plenty of enthusiasm.”