Sunil Chhetri managed a consolation goal in the last minute of the game after Brandon McDonald put the hosts ahead in the 38th minute and Travis Nicklaw doubled the advantage in the 62nd minute at the GFA National Training Center.
This was only their second World Cup qualifying win, the result coming less than a week after their upset 1-0 verdict over Turkmenistan in Group D.
Guam went ahead after 38 minutes when McDonald headed in Ryan Guy's long throw-in and Nicklaw extended the lead 24 minutes later when he received a long pass from his elder brother Shawn and fired home on the turn.
While Guam recorded their second win as many games in their qualifying campaign, 141-ranked India suffered their second straight defeat, the first being the 1-2 defeat to Oman at home last week.
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The latest reverse puts India's chances of a third-placed finish in the 2018 World Cup qualifying in jeopardy, which in turn could affect the country's prospect of earning a direct entry into the 2019 Asian Cup.
Guam, a United States island territory in the Western Pacific with a population of less than 200,000, are competing in the World Cup qualifiers for the first time since 2000 when they were beaten 19-0 by Iran and 16-0 by Tajikistan.
A total of 15 matches are being played throughout Asia today that serve as qualifiers for both the 2018 World Cup and the 2019 AFC Asian Cup.