Tony Parker added 17 points, including a crucial jumper in the final minute, as the Spurs held off a late rally to become the first team in this series to win on the road.
"We really believed we had a chance to win on the road here," said Spurs forward Tim Duncan, who had 16 points and 14 rebounds. "It's just a lot of confidence. A lot of games under our belt."
With a nucleus of Chris Paul, David West and Tyson Chandler, the Hornets appear destined for greater things, but now is not their time.
"One thing I want them to remember when they start working out next season is how they feel right now," said Hornets coach Byron Scott, adding he was proud of his team, which did not make the playoffs last season, for pushing the Spurs as far as it did.
"You have to go through some things before you can really understand how good it's going to feel when you get to that next level," Scott continued. "You don't go from not making playoffs to winning a championship. It just doesn't work that way. ... We're headed in right direction."
Now the Spurs and their championship ring-laden trio of Duncan, Ginobili and Parker will be traveling to Los Angeles to face the Lakers in Game 1 of the Western Conference finals on Wednesday night.
West led the Hornets with 20 points, while Paul and Jannero Pargo each added 18. Chandler had 13 points and 15 rebounds for the Hornets, who cut a deficit as large as 17 down to three inside the final two minutes.
While the Hornets managed to hold Duncan under 20 points by crowding the inside, his Spurs teammates combined for 12 3-pointers to keep alive their chance to win back-to-back titles for the first time.
"We knew the shots were going to be there. It happened today that we just made more," said Ginobili, who made four 3-pointers. "We just let it fly."
The win also gave Spurs coach Gregg Popovich 100 playoff victories, moving him into a tie with Larry Brown for third on the career list.
The Hornets had dominated the third quarters of their three previous home games in this series. This time, the Spurs, who have won four titles in the previous nine seasons, had an answer. It was their calling card: stingy defense.
The Hornets, down by nine to open the period, could not manage consecutive baskets throughout the quarter, never getting closer than seven.
New Orleans went nearly a three-minute stretch without a basket before Paul hit a pair of free throws to close the gap to 58-50.
Michael Finley then responded with a 3-pointer and Parker added a jumper, putting San Antonio up 63-50.
New Orleans finally began to look overwhelmed by the magnitude of the moment, even missing open shots. Peja Stojakovic shot an airball on an open 3-point attempt. West missed an open 12-footer. The Hornets shot 5-of-17 for the quarter.
"What we did today was play better D in the third quarter," Popovich said. "We held them down and it really was about that for us."
New Orleans continued to play solid defense inside, holding Duncan in check and limiting San Antonio to 6-of-18 shooting in the quarter. But that didn't help much with the Spurs hitting clutch shots from outside.
Finley added another 3, as did Robert Horry, and Ginobili's free throws gave San Antonio a 71-54 lead late in the period.
Buoyed by a home crowd that stood throughout the fourth quarter, the Hornets fought back to make a game of it, largely behind Pargo, who had done little in this series. He scored seven straight on four free throws sandwiched around a 3-pointer, pulling the Hornets to 81-77 with 3:10 to go.
Pargo made another 3 to cut it to 83-80 with about 1½ minutes to go, then attempted another for the tie with a minute left, but it rattled out.
Parker drained a jumper on the other end with 50 seconds left to make it 85-80, and New Orleans could not recover.
After a tight first quarter, the Spurs opened the second period with a 12-5 run, capped by Parker's driving layup as he was fouled, giving San Antonio a 36-25 lead.
Paul's driving floater off the glass turned the tide, sparking a 12-0 run that included 3s by Stojakovic and Morris Peterson. Stojakovic's baseline jumper briefly put New Orleans ahead 37-36, but Ginobili came back with a 3, Parker a driving layup and Duncan a short fade to put San Antonio right back in front.
Ginobili then hit two more 3s on consecutive possessions, restoring the Spurs' double-digit lead at 49-38 with under a minute to go in the half.
At that point, the Spurs were 8-of-15 on 3s, with Ginobili hitting four. The Hornets, by contrast, looked tight at times, missing five of nine free throws, with Paul missing three.
After Ginobili and Paul exchanged driving floaters in the final seconds of the half, the Spurs led 51-42.
Notes: The Hornets fell to 0-5 in second-round series. ... This marks the first time the Spurs have gotten past second round one season after winning a title. ... Home teams were 22-3 in the second round of this season's playoffs, with Detroit, the Lakers and Spurs getting the only road wins. ... A replay review wiped out what initially was called as a three-shot foul at the first quarter horn, when Ginobili was called for blocking on Paul's half-court heave. The replay showed time expired just before the foul and the release of the shot.