With Ken Condon's Romanised a non-runner and Coeur De Beaute withdrawn at the start, just three runners went to post for the six-furlong Group Two.
Fighting Irish (4-1), the winner of a nursery at Yarmouth three weeks ago, was joined by the Charlie Hills-trained Nebo and the only contender for the home team, French Pegasus.
Following placed efforts in the Superlative Stakes at Newmarket, the Richmond Stakes at Goodwood and the Mill Reef Stakes at Newbury, 4-11 favourite Nebo set a high standard and was sent straight to the lead from the off by Olivier Peslier.
However, Fighting Irish was always on his tail and picked up well for Cristian Demuro to secure a narrow victory.
The British pair were clear of French Pegasus in third.
Dunlop said: "It was a big jump up from a nursery to a Group Two, so we're absolutely thrilled.
"He's beaten a pretty good horse in Nebo and I thought Cristian gave him a brilliant ride.
"We've got him entered in the Criterium International at Saint-Cloud and after his performance today we'll take a close look at that.
"It would mean stepping up to seven furlongs, but I think it might be worth a bash."