The Grizzlies outscored the Spurs by 12 points in the third period but were unable to maintain their intensity in the fourth as the home side forced the game into overtime.
And the Spurs showed why they are one of the most devastating teams in the competition with a 12-8 run in the additional period.
Centre Marc Gasol led the Grizzlies with 20 points and Mike Conley was next best following his double-double (18 points and 12 assists).
Reigning NBA champions the Miami Heat powered past the Brooklyn Nets 102-89 on the back of a season-best performance from Dwayne Wade.
Wade scored 34 points and racked up seven assists as the Heat overcame a nine-point deficit at the half-time break.
Andray Blatche was the pick of the Nets players with 20 points and eight rebounds, while Gerald Wallace chipped in with 13.
Elsewhere on Saturday, Central division leaders the Bucks edged the Boston Celtics 91-88 in Milwaukee, Luol Deng hit 25 points as he guided the Chicago Bulls to a 93-88 victory over the Philadelphia 76ers and the Dallas Mavericks outclassed the Detroit Pistons with a dominant 92-77 win.
The Los Angeles Clippers extended the Sacramento Kings' winless away record to six, recording a convincing 116-81 triumph.
Jamal Crawford shot 17 points off the bench, while Blake Griffin and Chris Paul added 14 points each.
In one of the games of the season, the Portland Trail Blazers prevailed 118-117 against Cleveland in double overtime.
The Cavaliers led by two with 0.2 seconds remaining but Nicolas Batum sunk a three-pointer to hand the Trail Blazers a road victory.
Meanwhile, a 39-point final quarter inspired the Houston Rockets to a 124-116 win over the Utah Jazz, Oklahoma City eased past New Orleans 100-79 for their fifth win on the bounce and the Golden State Warriors got the better of the Indiana Pacers 103-92.