Has an NBA game ever ended 82-77?
It has. 82-77 has been a NBA final 23 times in 77,318 games. The first was Boston Celtics beat Philadelphia Warriors on February 23, 1950; the latest was Memphis Grizzlies beat Milwaukee Bucks on January 15, 2014.
That makes 82-77 the 898th most common final score out of 3,189 that have ever occurred in NBA. One point away, 83-77 has happened 24 times and 82-78 has happened 25 times. At one point the score disappeared for 39 years, between 1955 and 1994.