Gibson had eight assists and Joey Graham added 13 points off the bench as the Cavs (5-5) ended a two-game slide and got back to .500.
Cleveland outscored Philadelphia 26-16 in the third quarter. It was only the second time in 10 games this season that the Cavs have outscored their opponent in the third.
Thaddeus Young scored 17 and rookie Evan Turner 16 to pace the Sixers. Iguodala sat out with a troublesome Achilles' tendon.
Puzzled by Cleveland's third-quarter issues, first-year coach Byron Scott had joked that maybe the Cavs should repeat their dazzling pregame pyrotechnics after halftime to fire up his team. None of that was necessary. All it took was some better shooting, defense and effort.
It didn't hurt to have back energetic center Anderson Varejao. He had missed Cleveland's previous game with sore ribs.
The Cavaliers were without guard Mo Williams, who sat out his second straight game with a groin injury. But Gibson picked up the slack and Cleveland's bench chipped in 54 points.
With upcoming road games at New Orleans, San Antonio and Indiana, it was important for the Cavs to get a win - anywhere.
Owner Dan Gilbert seemed to sense the urgency. Before the game, he wrote, "We need to get this one tonight" on his Twitter page.
The Cavaliers got it by breaking open a back-and-forth game with an 11-0 run in the third, highlighted by a three-point play from Varejao that came after Anthony Parker's hustle.
Parker ran down a loose ball as he fell out of bounds and delivered a blind, behind-the-back pass to Antawn Jamison, who flipped the ball to Varejao. Cleveland's center scored, was fouled and made his free throw give the Cavaliers a 72-61 lead.
Philadelphia twice got within seven in the fourth, but Gibson hit a big 3-pointer and a jumper to push Cleveland's lead back to 13 with 5:07 left.
The third quarter has been Cleveland's downfall all season. Entering Wednesday's game, the Cavs had been outscored 226-164 in the third.
Elton Brand had 13 points and 11 rebounds. Turner, the former Ohio State star, added nine assists and Jrue Holliday had 10 assists for the Sixers.
Andres Nocioni's 3-pointer with 2.2 seconds left tied it at 54 at the half and sent the teams to their respective locker rooms looking to figure out how to get their offenses untracked.
Still not fully schooled in Scott's "Princeton" offense, the Cavaliers shot just 35 percent in the first quarter but responded by going 13 of 21 from the field in the second.
Turner had seven points at half - two more than his previous two games combined.
Notes: Back in Ohio, Turner received a loud ovation from Buckeye fans during pregame intros. While in town, he visited his favorite breakfast spot: Waffle House. "They don't have them in Philly," said Turner, who ordered a double waffle, sausage and hash browns. ... Scott's relationship with Sixers coach Doug Collins dates back to his playing days at Arizona State, where Collins was an assistant coach. "It was one of my great joys," Collins said. "Byron was a tremendous talent. I felt like I had a chance to help him with his career, which makes me feel good." ... Longtime Cavaliers radio play-by-play broadcaster Joe Tait was released from the hospital after a lengthy stay for a blood clot in his lung.