Isner, ranked 18th, was coming off a third-round Wimbledon exit at the hands of reigning US Open champion Marin Cilic after dropping the fifth set 12-10. He was seeking a third title at Newport and the 10th ATP crown of his career.
Isner blasted 21 aces with only a lone double fault but Ram fired 18 aces back and rallied after dropping the first set tie-breaker, taking the only break of the second set and outlasting the top American after neither broke in the last.
Also defeated was US eighth seed Tim Smyczek, who fell 6-3, 6-4 to Czech Jan Hernych.
Two other US seeds advanced with number four Jack Sock dumping Czech player Radek Stepanek 6-2, 6-0 and number six Sam Querrey dispatching Australian Matthew Ebden 7-6 (7/3), 7-6 (7/1).
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Next up for Sock will be Slovakia's Lukas Lacko, who defeated Belgium's Niels Desein 6-3, 3-6, 6-2. Querrey's second-round foe will be German Dustin Brown, who beat Adrien Bossel of Switzerland 7-6 (7/4), 6-3.
Rain delayed the start of the final first-round match between French fifth seed Adrian Mannarino and German wildcard Tommy Haas.
Haas won the first set 7-6 (7/5) and Mannarino the second 7-6 (7/1) before darkness halted play, leaving France's Edouard Roger-Vasselin to await the winner after eliminating Slovenia's Blaz Kavcic 4-6, 6-3, 6-2.