West scored seven points in the fourth quarter, hitting five of six free throws to help the Pacers hold on.
"David always comes through when we need him most," George said. "He shines in those moments. He really picks us up in those moments."
Brooklyn tied the score at 76 on Livingston's two free throws with 10 minutes left, but Hibbert converted a three-point play and Indiana led the rest of the way.
Livingston pulled Brooklyn to 85-83 with 5:10 to play, but after an extended Indiana possession, Stephenson hit two free throws after being fouled by Johnson, then Hibbert slammed home a dunk.
The Nets wouldn't go away, though. Hill hit one of two free throws with 18.6 seconds to play for a 94-90 lead before Johnson's 3-pointer with 8 seconds left made it 94-93.
West then hit two free throws, rebounded Pierce's missed 3 and hit one more free throw to make it 97-93. Williams hit a 3 with 0.4 seconds left, and the game ended after Scola threw the inbounds pass off Pierce's back.
"The one thing we said was, 'Don't throw it out of bounds,'" Vogel said. "We said, 'Throw it anywhere where it hits them or us.'"
Brooklyn took advantage of a sluggish start by the Pacers to lead by seven points three times in the first quarter, the last on Johnson's short jumper that put the Nets ahead 13-6 with 7:28 to play in the period.
The Pacers took their first lead at 19-18 on George's 3-pointer. Livingston hit two jumpers and Johnson added another to put Brooklyn back ahead 24-19, but Indiana closed the quarter on a 6-0 run to lead 25-24.
Neither team could build a lead greater than four points in the second quarter, and the lead changed hands six times, with five ties. George's driving layup with 6 seconds to play gave the Pacers a 46-45 halftime lead.
The Pacers outscored Brooklyn 12-2 over the first 3:36 of the third quarter, building a 58-47 lead and prompting a timeout by Kidd.
Brooklyn responded with a 19-9 run to pull to 67-66. Indiana scored the next five points, but Alan Anderson hit a 3-pointer, Mason Plumlee made one of two free throws and the Nets trailed just 72-70 entering the fourth.
NOTES: The Pacers improved to 32-1 when leading after the third quarter. ... Indiana missed four of its first seven shots.