Indianapolis native George Hill led San Antonio (4-3) with 21 points, while Duncan added 15 points and 11 rebounds.
The teams were even through the first 6 minutes of the third quarter of the game played at Indiana University's Assembly Hall.
Hibbert got the Pacers going when he went baseline and reverse dunked on Duncan for a 72-71 lead. He followed with a mid-range jumper and a layup to give Indiana a 78-75 lead and force a San Antonio timeout.
Hibbert came right out of the timeout with a layup to keep the momentum going. Jones hit a baseline jumper with 1 second left in the period to give Indiana a 92-82 lead. The Pacers outscored the Spurs 34-21 in the third quarter to erase a 3-point halftime deficit.
Hibbert enjoyed his matchup with Duncan.
"It was fun to get out there and play hard and get that many chances against a skilled center like Tim Duncan," Hibbert said. "He has a very polished game. That's something I want to get to."
But the other side of his game is the constant foul trouble. He committed two in the third quarter and fouled out after playing only a minute in the fourth.
Hibbert was the team's No. 2 scorer in the preseason, but he was second in personal fouls and disqualifications. He was hounded last season by foul trouble during a promising, but frustrating rookie campaign.
"He's capable," Pacers coach Jim O'Brien said. "He needs to play defensively, keeping in mind that he needs to go straight up instead of trying to block shots down. That's where he gets in trouble. He knows that, and he's getting much better at that."
Indiana's perimeter game complemented Hibbert's second-half effort. The Pacers were 7 of 12 from 3-point range in the second half after making just 4 of 18 in the first.
The Pacers led 114-110 before Hill made a layup with 18 seconds left. Indiana turned it over to give San Antonio a chance to tie or win, but Keith Bogans missed an off-balance jumper as time expired.
The Spurs got hot early in the fourth quarter and cut Indiana's lead to 96-94, mostly with reserves, before Granger made a 3-pointer and a layup to push the lead out again. San Antonio never regained the lead.
"The energy and activity were great," San Antonio coach Gregg Popovich said. "The young guys were learning and making the right kind of mistakes. They gave us some good play on the road."
The Pacers survived, but that wasn't enough to satisfy O'Brien.
"We got a long way to go, brother," he said.
Indiana had only 10 active players because of injuries. Gs Travis Diener, Mike Dunleavy, T.J. Ford and Luther Head and F Tyler Hansbrough all sat out. ... The Spurs had no one on the injury report. ... The Pacers announced earlier Friday that Mel Daniels, the longtime director of player personnel, was no longer with the team. ... Indiana University coach Tom Crean attended the game.