Bain, the leading Scotsman in the 2007 Open at Carnoustie, signed off with a two-under 70 at the Springfield Village course and claimed the 12th of 40 tour places up for grabs with an eight-under 279.
Dunn closed with a three-under 69 for a 282 and qualified comfortably in a share of 25th behind eventual winner, Artemio Murakami, who edged out Guido Van Der Valk in a play-off after both players had tied at the top on 275.
Advertisement
Hide AdAdvertisement
Hide AdLee Harper, the former Scottish Boys' champion, failed to make the grade on 295 after a 79 while Jean Van De Velde, runner-up in the 1999 Open, also missed out on a 288.