Tony Parker added 21 points, seven assists and three steals for the Spurs, who have won five straight and consecutive road games -- both against Memphis -- for the first time since March.
"We made some shots and got some stops. Then in the fourth quarter, we just couldn't make a shot anymore. They (Spurs) were hurting us in the pick-and- roll and just kept getting what they needed. It was a close game. We just couldn't get the stop and when we got the ball, we just couldn't finish on the offensive end," Memphis head coach Lionel Hollins said.
Duncan's three-point play and dunk on consecutive San Antonio possessions gave the visitors an 87-81 lead with 1:18 to play.
Conley banked in a three-pointer to make it 87-84 with 1:10 left, and Memphis got the ball back after Duncan's offensive foul.
Following a Gasol missed layup, the Grizzlies regained possession after a jump ball between Gasol and Gary Neal. But Rudy Gay's step-back three-pointer from the top of the arc was an airball.
Danny Green nailed a pair of free throws with 8.5 left to seal the win for the Spurs.
"All our young guys are playing well. It's going to help us down the road," Parker said.
San Antonio nailed all four of its attempts from beyond the arc in the first quarter and took a 26-18 advantage into the second.
The Spurs continued to hold a comfortable margin in the second before taking a 52-46 lead into the break.
With the Spurs up 61-48 with 8:44 to go in the third, Memphis closed the stanza on a 25-6 surge. Josh Davis nailed a trey with 1.4 to play in the quarter as Memphis led, 73-67, going into the fourth.
But San Antonio netted the first nine points of the final period as James Anderson capped the flurry with a three-pointer, giving the visitors a 76-73 lead with 7:29 to play.
The Spurs last won consecutive road games on March 2 and 12...Monday marked the first game of a nine-game road trip for San Antonio...The Spurs finished 7-of-16 from beyond the arc...The Grizzlies scored 22 points off 19 San Antonio turnovers.