Parker, who finished with only one turnover in 36 minutes, had 10 points while shooting 5 for 5 in the final quarter.
The Spurs held the Hornets to 38 percent shooting in the second half while improving to 19-2 at home this season.
Parker's layup gave the Spurs a 72-70 lead, their first since leading 9-8 2 minutes into the game. The advantage was short-lived, as the Hornets went on a 7-0 run.
Ginobili, making his first start after missing three games with a strained hamstring, had five points in the final quarter.
"It was huge that Manu played," Parker said. "Even if it was for 15 or 16 minutes, it was big minutes. He looked good. He didn't go full speed. I think he was trying it (hamstring) and testing it. In Dallas (on Friday), he's going to get more aggressive."
San Antonio started 4 for 11 on free throws, but offset it somewhat by going 7 for 16 on 3-pointers.
Splitter scored eight of the Spurs' first 10 points, with Parker picking up assists on three of the layups. Splitter drew two fouls on top draft pick Anthony Davis in his run.
NOTES: Duncan missed only his second game of the season due to injury. Duncan first sat out Nov. 29 in Miami, along with Ginobili, Parker and Green. The quartet was sent home by Popovich, leading the NBA to fine the Spurs $250,000 for what Commissioner David Stern termed a "disservice to the league and our fans." . San Antonio signed Australian national team member Aron Baynes, a 6-foot-10 post. Contract terms were undisclosed. Baynes was averaging 13.8 points and 9.8 rebounds for Union Olimpija of the Slovenian Basketball League prior to signing with the Spurs. . Texas Rangers manager Ron Washington and players Ian Kinsler, Derek Holland, Josh Lindblom Brandon Snyder were in attendance. They were in San Antonio to promote the "Big League Weekend," a two-game, spring-training series against the San Diego Padres at the Alamodome. The series marks the first baseball games at the Alamodome, the former home of the Spurs. . Houston Astros players Brett Wallace and Jose Altuve were in attendance as part of the team's Winter CAREavan to promote their upcoming season, their first in the American League. Unlike the Rangers, who were sitting in box seats on the second level, the Astros were sitting courtside.