Thomas Hobson, runner-up to Desert Skyline in last year's renewal of the Group Two contest, was the 2-1 favourite to go one better under Ryan Moore, who settled his mount at the rear of the field for much of the two-and-a-quarter-mile journey.
Max Dynamite, best known for his narrow defeat in the 2015 Melbourne Cup, was ridden a little more prominently by Andrea Atzeni and quickened to lead approaching the final two furlongs.
However, Moore covered the move aboard the strong-travelling Thomas Hobson and while his stablemate did not go down without a fight, the market leader always looked the stronger and won the battle by a cosy half a length.
The pair were seven lengths clear of Sheikhzayedroad in third.
Mullins was at Listowel, where he told Press Association Sport: "We had thought both horses were working better at home than they had been running, so it's great to see their home work coming out in them.
"I doubt they'll run before the Melbourne Cup, but I haven't spoken to Rich yet. I imagine that books their tickets there.
"I imagine Thomas Hobson winning will put him way up the order of entry, as they call it there, and last year he got in - he was sixth last year from a draw which was way-out wide.
"Hurdling is not on either horses' agenda at the moment and we'll play their Flat cards while they are young eight-year-olds!"
Regarding holding on to Moore's services in Melbourne, Mullins said "Ballydoyle might have a few more entries this year, so we'll see."
David Simcock said of Sheikhzayedroad and also Algometer, who was fourth: "I was pleased, Algometer just lost a bit of momentum slightly.
"I've got a feeling he'll be a nice two-miler, especially next year when we can set our stall out and start somewhere like the Sagaro.
"Sheikhzayedroad will probably have one more run, but he'll be better for having that under his belt."