In the saddle of Boisterous, Velazquez added another Group 1 triumph to his stunning record, scoring his first big win at Belmont Park a year after his Belmont Stakes success.
Pan American Stakes winner Twilight Eclipse came in second with Exclusive Strike taking third.
"I'm going to smile on this one, because this horse deserves to win a grade I," McGaughey said of Boisterous.
"He had been training so good. We kind of caught a turf today we liked. I was looking for a little bit of rain. I'm tickled to death, not for me, but for the horse."