Tagula, who won Newmarket's July Stakes on his previous outing, beat the French-trained hot favourite With Fascination by a length to earn a quote of 25-1 for next year's 2,000 Guineas from William Hill. His immediate target is the Middle Park Stakes back at Newmarket on 28 September.
Third place went to Andre Fabre's representative, Barricade, with the Peter Chaple-Hyam-trained Russian Revival - who had made the running until the furlong pole - fading into fourth.
Clive Brittain's World Premier finished sixth and Richard Hannon's Prix Robert Papin winner, Lucky Lionel, a disappointing seventh of the eight starters for the pounds 96,000 first prize.
Swinburn, who dropped his whip in the closing stages, was in ecstatic mood after the race. "I got a perfect lead from Cash (Asmussen) on the favourite. A furlong out I thought I might win, but I didn't realise how well he would respond.
Balding said of Tagula: "This horse has plenty of speed at six furlongs but he is so relaxed that he should get the mile without any problems next year."
David Loder's Tillandsia narrowly failed to complete a British double when going down by a head to Balanka in the Coupe du Fonds Europeen de l'Elevage. The winner now heads for what is always an informative trial for the Prix de l'Arc de Triomphe, the Prix Vermeille.
Hernando, the 1994 Arc runner-up who made a successful seasonal debut in the Prix Gontaut-Biron at Deauville on Saturday, is 10-1 with Ladbrokes for this year's renewal. His prep race may be Leopardstown's Champion Stakes on 9 September.
Prix Morny (6f, Group 1)
1. TAGULA bay colt Taufan - Twin Island W R Swinburn
2. With Fascination brown filly Dayjur - Fran's Valentine C Asmussen
3. Barricade bay colt Riverman - Balleta T Jarnet
Also ran: Russian Revival (4th), Shining Molly (5th), World Premier (6th), Lucky Lionel (7th), Sangria (8th).
8 ran. 1, 3/4. (Trained by I Balding, at Kingsclere, for Mr & Mrs R Hitchens). Pari-Mutuel: 9.70; 2.10, 1.40, 1.50. DF: 17.40.Reuse content