Min claimed a deserved Grade One success at Cheltenham by landing the Ryanair Chase.
Second in a Sky Bet Supreme and Betway Queen Mother Champion Chase, he travelled strongly at the head of affairs under Paul Townend turning for home.
Market rival A Plus Tard hadn't jumped with his usual fluency but was still in there pitching while Saint Calvados was on the bridle on their heels.
He was to emerge as the main threat and closed the leader down in the final strides, but Min was always doing enough, scoring by a neck.
Townend said on ITV Racing: "We went pretty hard early on but then we steadied it down and Min got into a great rhythm. It's very important to win here, it's a big week. I've been coming here a long time and coming here with good rides so just had to approach it the same manner."
When asked if it was hard to perform with former Mullins' number one jockey Ruby Walsh watching on from the ITV podium, he added: "No, it's easier to win when he's watching!"
Mullins said: "He's been a super horse for us and it's great he's had his day here. We used the wrong tactics on him in the Champion Chase last year and it didn't work out. He likes to be up there, Paul let him do that and here he is again at the top table.
"I was very worried when Saint Calvados came up - we seem to be opening the door up the inside a lot this week! I did get very worried, but he threw a lovely leap at the last and put it to bed. He still had a little bit left in the tank. I'm wondering does he just get that trip, is that the extent of his stamina? I think he could come back to two miles, but this seems to be his optimum."
He added: "It's important to have winners here, but the horses are running well. We're just not getting the rub of the green. Melon was beaten a nose in the first and Faugheen ran great. They're all running well, so we just keep our fingers crossed for better luck for the rest of the day and Friday."
On Townend, he said: "He's very cool. Paul just forgets the last race - his attitude, 'next race, let's concentrate on that and not worry about the bad things that happened'. He just concentrates on what he has to do."
Harry Whittington said of Saint Calvados: "I'm so proud of him, I could feel how well he was saddling him and I knew he was going to run a big race. Jamie Neild rides him every day and he said this week he was ready to bring the house down.
"The change in tactics has worked and he's still unexposed, he can go up in trip again next year. I'm gutted, but so thrilled for the horse. Coming to the last I thought we had a chance, but the door was closed on him. It's fine margins, Gavin (Sheehan) gave him a peach. We're inching closer (to a first Festival winner)."
Paul Nicholls said of fourth-placed Frodon: "Those two-milers are too sharp for him and Bryony (Frost) said he was flat out all the way, so we will step him back up to three miles. If we go to Aintree we will run him over three miles in the Bowl.
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