Lahiri, who is making his fourth appearance in five years at the Open Championships, had three birdies against one bogeys along the famous Scottish links.
Lahiri, playing alongside Sergio Garcia and Keegan Bradley, birdied the second, fourth and seventh holes, while he dropped a shot on the fifth.
Lahiri has made the cut twice in his previous three starts in the Open, with tied-30th last year as his best. His best in a Major is tied-fifth at the PGA Championships last year.
Four other Americans -- Tony Finau, Bill Horschel, Steve Stricker and Justin Thomas -- finished their rounds with fine scores of four-under 67 each.
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Defending champion Zach Johnson was also four-under through 10 holes, while Justin Rose started with 68) and Rory McIlroy and Rickie Fowler opened with 69 each. McIlory had four birdies in the stretch between fourth and eighth, but dropped a double on 13th and a bogey on 14th to end with a 69.
Meanwhile, Thailand's Thongchai Jaidee birdied the 18th hole to begin his campaign at The Open with a level par 71 on Thursday but there was disappointment for countryman Kiradech Aphibarnrat and Korea's Jeunghun Wang.
Thongchai, a triple Asian Tour number one, carded two birdies on the card against a double bogey on the 15th hole at Royal Troon when he found two pot bunkers.
Big-hitting Kiradech endured a tough finish where he dropped four shots over his last four holes to sign for a 75 while Wang, a two-time winner this season, had five bogeys for a 75 which marred his debut at the world's oldest Major.