Has an NBA game ever ended 77-75?
It has. 77-75 has been a NBA final 19 times in 77,318 games. The first was Philadelphia Warriors beat Detroit Falcons on March 20, 1947; the latest was Oklahoma City Thunder beat Los Angeles Lakers on May 16, 2012.
That makes 77-75 the 1001st most common final score out of 3,189 that have ever occurred in NBA. One point away, 78-75 has happened 15 times and 77-76 has happened 12 times. At one point the score disappeared for 48 years, between 1954 and 2002.