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The 18th-ranked Isner won the title on Newport's grass in 2011 and 2012.
The 161st-ranked Ram, who won the tournament in 2009, closed the match with a forehand winner after Isner slipped on the wet grass with a light rain falling.
Isner saved two match points before Ram went up 9-8 when the 6-foot-10 American hit a shot wide, losing his third service point of the tiebreaker.
''I just didn't play well enough to win,'' said Isner, pushing aside the match stats without wanting to look. ''I didn't serve well in pockets. There were times where I would miss five, six first serves in a row. That's not good. He served well and on these courts anything can happen.''
Isner had won 15 of his 19 previous matches at Newport. He came into the tournament after matching his best showing at Wimbledon by reaching the third round.
''It's good that I've won here before. I love it here. I love the city,'' he said. ''It can happen like that. Two guys that serve well and it can happen. I just lost the close points.''
Isner has been seeded No. 1 on 15 occasions in his career at an ATP event, posting a 34-9 record before the loss.
It was the first opening-round matchup of former champions in the 39-year history of the tourney.
''We don't have anywhere else like this on tour where my game sort of fits as well as it does here,'' the 31-year old Ram said. ''It just makes it where I have a better chance of having higher-ranked wins here than anywhere else. It's sort of suited more old-school style tennis, and I feel like I can play that pretty well.''
Ram asked the chair umpire to check the surface after the 10th point of the tiebreaker. The chair umpire felt the grass near the same area where Isner later slipped, allowing play to continue.
Asked if it was the conditions that caused him to slip, Isner said: ''Yeah. It was the first time I slipped.''
In other play, fourth-seeded Jack Sock beat Radek Stepank of the Czech Republic 6-2, 6-0. The 22-year old American won in 58 minutes.
No. 6-seeded Sam Querrey of the U.S. beat Matthew Ebden of Australia 7-6 (3), 7-6 (1); Germany's Dustin Brown, coming off a second-round upset of Rafael Nadal at Wimbledon, defeated Adrien Bossel of Switzerland 7-6 (4), 6-3; and qualifier Jan Hernych of the Czech Republic upset No. 8-seeded American Tim Smyczek 6-3, 6-4.