Vauban, who settled just behind the leaders before cruising to the front around 550m from home and holding a margin of more than a length for the last 400m, scored by 1-1/2 lengths from Valiant King with Peking Opera 4-1/2 lengths back third.
Ryan Moore rode Vauban at Royal Ascot and is the leading contender for the Melbourne Cup provided Vauban is allocated enough weight, but Colin Keane was in the saddle at Naas and the Irish jockey declared his availability for the ride at Flemington.
"I'm sure I could make myself available if needs be," Keane said.
"I'm not sure (if he's a Melbourne Cup horse) because I've never been there, but he ticks a lot of boxes; he stays well, he's very uncomplicated, he's won on quicker ground at Ascot and he handled slow ground here today, so you'd like to think he ticks a lot boxes."
The Ballyroan Stakes was the first Group success on the flat for Vauban, a multiple Grade 1 hurdle winner, and Casey said Mullins' attention would now turn to determining whether to give the son of Galiway another start in the UK or have his next run at Flemington.