San Antonio is 18-1 this season when they have led after the third period and went 9-0 at home in December.
The Spurs went on a 12-4 run late in the first behind the speed of their backcourt. Parker fed Splitter for a dunk and Boris Diaw for an uncontested layup after drawing the defense on consecutive drives. Ginobili scored a pair of layups, including one after he stepped in front of a pass.
Coupled with their 111-86 victory over the Dallas Mavericks on Sunday, San Antonio has now swept six back-to-back games this season and is 11-5 in those contests.
The Spurs hit the road for back-to-back games at Milwaukee on Wednesday and Thursday at New York.
The lopsided third quarter allowed San Antonio to limit its minutes Monday night. No Spurs players put in more than 26 minutes.
"It was very important for us, especially since we have a long trip tomorrow," Ginobili said of the rest. "We are going through a tough stretch but it is great to have a chance to sit most of the fourth tonight."
NOTES: Spurs G Gary Neal (strained right calf) missed his fourth straight game and sixth this season. . Brooklyn F Gerald Wallace (bruised left knee) missed his eighth game of the season. . Johnson, Andray Blatche and C.J. Watson are the only Nets to play in every game this season. Johnson has started each of those games. . The fewest points an opponent has scored in any quarter is three by Denver during the opening period on Nov. 27, 2002. . The Nets have not won in San Antonio since Jan. 22, 2002, a streak of 11 games. . Carlesimo was Popovich's lead assistant with the Spurs from 2002-2007 before leaving to become head coach of Seattle in 2007. The SuperSonics moved to Oklahoma City the following season, where Carlesimo was fired 13 games into the season.