Jockey Eddie Castro patiently eased the 7-year-old son of With Approval four or five wide, advancing on the far turn and then moving eight wide to make a stretch run. Second-place Aragorn brushed the side of the gate at the break but settled down to battle Miesque's Approval at the top of the stretch before fading.
Badge of Silver finished third and Sleeping Indian, fourth.
The win was the first in the Breeders Cup series for Castro.
"That's the way he's run all year. He deserved it," winning trainer Marty Wolfson said of Miesque's Approval.
Miesque's Approval covered the one mile on grass in 1:34.75 to take home $1.17 million of the $2.17 million purse.
Miesque's Approval paid $50.60, $17.20 and $10.40; Aragorn, $5.80 and $4.40; and Badge of Silver, $9.80. The $2 Exacta paid $246.