Answer: 1888
To be fair, the entire 1887 season was one game--a November 13 meeting between Virginia and Pantops Academy (a private school in Charlottesville, VA). That meeting between the two schools ended in a 0-0 tie. The next year, November 20, 1888, Virginia defeated Pantops Academy in a re-match, 20-0. The team would also suffer its first defeat (and first intercollegiate) game against Johns Hopkins University on December 4, 1888, 36-0. For the 1888 season, the team went 2-1.