The Western Conference leaders trailed by three points after the first quarter and by just one at the end of the half, but they seized the initiative thereafter.
Tony Parker led the way for the Spurs with 27 points in a tense encounter that condemned New Orleans to their sixth straight defeat.
Jonas Valanciunas contributed 17 points and 10 rebounds as the Toronto Raptors eased past the Milwaukee Bucks 116-94.
Kyle Lowry also poured in 23 points to pile more pressure on the Bucks, who have lost their last six matches and have just one win in 10.
The Chicago Bulls' winning streak came to an end at five matches after they suffered a comprehensive 102-88 defeat against the Washington Wizards.
John Wall and Nene both scored 19 points apiece with the latter contributing a vital eight in the final period to quell any hopes of a comeback from the Bulls.
A virtuoso performance from Carmelo Anthony inspired the New York Knicks to a 98-96 overtime victory over the Phoenix Suns.
The former Denver Nuggets man notched 29 points, including four of the Knicks' six in overtime, and 16 rebounds to edge his side to their fifth win on the trot.
Dwight Howard propelled the Houston Rockets to a 104-92 victory over the Boston Celtics with 32 points and 10 rebounds.
The Dallas Mavericks beat the Orlando Magic 107-88, with Monta Ellis bagging 21 points, while Alec Burks scored a career-high 34 points as the Utah Jazz eased to a 118-103 triumph over the Denver Nuggets.