Battier (10 points) connected on a trey with 23 seconds remaining to put the Grizzlies ahead 99-98 and Tony Allen hit a pair of free throws in the closing seconds, icing the first playoff victory in franchise history for eighth-seeded Memphis.
Zach Randolph led the Grizzlies with 25 points and 14 rebounds and Marc Gasol added 24 and nine as Memphis shocked top-seeded San Antonio and took a 1-0 lead in their Eastern Conference quarterfinal series.
Mike Conley chipped in with 15 points and 10 assists for Memphis, which shot 55.2 percent from the field in the win.
Tony Parker notched 20 points on 4-of-16 shooting for the Spurs while Tim Duncan added 16 points and 13 rebounds.
Richard Jefferson missed a potential game-tying 3-pointer at the buzzer for San Antonio.
Celebrity Breakups and divorces of 2014 [PHOTOS]