The U.S. Masters champion picked up four birdies and an eagle to move within one stroke of joint leaders Paul Peterson of the United States, Frenchmen Mike Lorenzo-Vera and Gregory Havret and England's Daniel Brooks.
Willett's effort was by far the best of the European Ryder Cup players who are competing at Crans.
Former world number one Lee Westwood opened with a two-over 72 while fellow Englishmen Matt Fitzpatrick and Andy Sullivan slumped to a 75 and 74 respectively.
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England's Chris Wood, who won the PGA Championship at Wentworth in May, carded a 69.
Holders Europe will be aiming to win the Ryder Cup for the ninth time in 11 editions when they take on United States at Hazeltine, Minnesota from Sept. 30-Oct. 2.
(Writing by Tony Jimenez; Editing by Toby Davis)
