Rutgers first Thanksgiving Day game started at 11:00 p.m. on November 30, 1899 against the Knickerbocker Athletic Club who they lost to 11-0. The game was played inside Madison Square Garden II (50 cents admission).
Rutgers won Thanksgiving Day games in 1914, 1915, 1941, 1947, 1976 and tied in 1936. They lost in 1916, 1920, 1937, 1939, 1940, 1963 and 2004.
Rutgers played its first games off the continent when both the Rutgers football and basketball teams and 2,000 followers finished the 1974 football season with a November 30 game in Hawaii. It was the first time Hawaii had ever played an east coast school. On Friday night before 7,495 at the Honolulu International Center (1:15 a.m. in New Brunswick), the men’s basketball team upset Hawaii 75-70 with Phil Sellers scoring 24, Mike Dabney 23 and Hollis Copeland 18 points. Fans were annoyed at the officiating and when the football team played Saturday night (12:15 a.m. in New Brunswick) the play was termed dirty and the crowd rowdy. Rutgers lost 28-16 before 16,306.
I am not aware of the Rutgers men's basketball team playing on Thanksgiving Day itself although playing the night before and the days after are not uncommon.