The frustrated Pelicans also drew three technical fouls during the Pacers' third-quarter run — one each to Davis, Jrue Holiday and assistant coach Dave Hanners — the last two after a foul call on Holiday.
Gordon scored just two points in the third quarter. Ajinca converted both of his field goals in the period, but the rest of the Pelicans missed 12 of 14 attempts.
"We just didn't play that well," Pelicans' coach Monty Williams said. "Basically, they took it to us on the defensive end, and I thought offensively Stephenson was the catalyst for them.
"We just got out of sync on the offensive end, and that led to them getting a number of offensive opportunities. They just picked up, and we did not."
Indiana made 11 of 16 field goals (68.8) in the decisive quarter.
"They came out and played a great first quarter, and we buckled down the rest of the way," said Pacers' coach Frank Vogel. "We wanted to mix up the matchup on Gordon, give him a different look.
"We adjusted our offensive package a little bit to get more efficiency. What we showed in the third quarter is who we are: we're a high-powered offense with some shot-makers."
The Pelicans put together a 12-0 run over a 3:08 span in the first quarter to push a two-point lead to a 27-13 advantage 2:30 before the break. Davis hit a jumper and drove the baseline to pace the surge.
Watson hit a 15-foot jumper, Luis Scola sank a jumper from the right side and Watson made a 19-footer as Indiana responded with a 6-0 burst in under a minute early in the second period to close to within eight points.
Gordon scored his 17 first-half points on 7-of-11 shooting, including 3 of 4 from beyond the arc as the Pelicans led 49-44 at the half.