Trained by Willie Mullins and ridden by Paul Townend, the nine-year-old was all-out to secure a neck success in the £350,000 event, seeing off the gallant Saint Calvados (16/1). The 7/4 favourite A Plus Tard was a length and a half behind in third.
On his fourth appearance at The Festival, this was Min's first success at the meeting with his other efforts including second-placed finishes in both the Grade 1 Supreme Novices' Hurdle (2016) and G1 Racing Post Arkle Novices' Chase (2017).
In a remarkable career, Min is now a six-time Grade 1 winner and has also finished runner-up in six Grade 1 contests. Closutton maestro Mullins was recording his second victory of the week and 67th winner in total at The Festival.
He said: "It was a good performance from Min and he likes to race from the front.
"We got the tactics wrong on him last year [finished fifth, Betway Queen Mother Champion Chase] and it didn't work out. We changed things up this year and learnt our lesson - here he is now back at the top table.
"Min threw a wonderful leap in at the last and it was a great effort.
"Watching him jump today, he was just fantastic through the air and, when he needed a jump, he got them. He put the others under pressure.
"It was probably wobbly knee time after the last when Saint Calvados came up the inside but he still had a little bit left in the tank.
"I wondered whether Min just gets that trip and if that is the extent of his ability. I think he could go back to two miles but this seems to be his optimum trip.