The game was close down the stretch but Batum drained two free throws with 9 seconds left, handing the Blazers a seven-point lead.
Tim Duncan cut the Spurs' deficit to four with a 3-pointer, but Batum then iced the win with long trey of his own to complete his triple-double.
Damian Lillard provided 25 points, seven rebounds and seven assists as Portland improved to 2-1.
LeMarcus Aldridge added 24 points and Wesley Matthews contributed 20 for the Blazers.
Duncan, returning after a one-game injury absence, finished with 24 points for the Spurs.