Boozer shot 12-of-16 from the field and Harpring was 7-of-12, helping Utah overcome early shooting woes and finish the game at 54 percent.
"The last three or four games since the break, he's been killing them," Boozer said. "You get that kind of production off the bench, that's incredible."
Utah already trailed by 12 points when Harpring entered in the first quarter, but his impact was immediate.
"We've got certain plays, that when we run them, they're tough to guard," Harpring said. "If you set screens and run them the right way, we can be a tough team to guard."
"We pushed him off the lane and made him take tough shots over our hands or made him make tough passes," Okur said.
Mike Miller added 17 points for Memphis, while Hakim Warrick finished with 13. Memphis, one of the best 3-point shooting teams in the league, had a poor night outside the arc, hitting only three of its 20 long-range shots. That included Miller going 2-of-12.
Utah, which trailed by as many as 16 in the first half, pulled even in the third, and put together a 33-10 run spanning the third and fourth quarters to build the lead to 95-77. From there, Utah maintained the advantage for its ninth win in the last 11 outings.
Meanwhile, Memphis dropped its second straight and has lost five of six.
Okur scored 16 points for the Jazz, while Deron Williams finished with 14 points and 10 assists.
Utah missed its first six shots and didn't make its first field goal until Boozer's layup with five minutes gone in the opening quarter. That helped Memphis open a 10-0 lead, which the Grizzlies eventually extended to 16 points.
Memphis led 49-44 at the half as Gasol already had 22 points and nine rebounds. But the Grizzlies had squandered a double-digit lead as Okur, who missed his first four shots, hit a pair of baskets in the final 30 seconds. Memphis coach Tony Barone saw the game start slipping away at that point.
"They wore us down," Barone said. "We let them get five points at the end of the first half, and that swung the momentum. The key to the game was their ability to physically wear us down. They play a physical game, and we didn't react well to that."
Harpring provided an early spark off the Utah bench, scoring 15 points in the half, while Boozer hit his first four shots en route to 12 points before intermission.
"We would not have been in the ballgame at all if (Harpring) didn't have a terrific first half," Jazz coach Jerry Sloan said. "...Everybody looks to him because he knows how to get open. If I was a young player, I'd watch Matt Harpring play because he works hard to get open and shoots the shot when he gets it."
Meanwhile, Memphis continued to feed Gasol in the half, running much of the offense through its leading scorer. He shot 7-of-10 in the half.
The Jazz stayed within a basket through the early minutes of the second half thanks to Okur's better shooting. He was limited to the closing five points in the first half, but hit his first four shots after the break and scored 11 in the third period. His 20-footer with 3:02 left in the third pulled the Jazz even at 67.
Harpring followed with a pair of free throws to give Utah its first lead of the game, and the Jazz used that as part of a 15-4 run to close the period and build a 77-71 lead entering the fourth.
"Obviously, we didn't shoot the ball well and we settled too much when we had a nice lead," Gasol said. "We should have kept attacking them and try to put them away early.
"We gave up too many easy baskets in the second half; too many easy layups and fast break points."
Boozer's minutes are still somewhat limited after he missed eight games with a left leg injury. Utah coach Jerry Sloan said he hoped his leading scorer's time would increase from the seven minutes a quarter Boozer played in Monday's loss to the Lakers. Boozer played 36 minutes against Memphis. ... Williams was back in the starting lineup for Utah after missing Monday's game with a strained left groin that has nagged him since he was injured in the Rookie Challenge game during All-Star weekend. ... Memphis was without F Brian Cardinal, who had arthroscopic surgery on his left knee on Tuesday, and is out for the season. ... Memphis G Chucky Atkins left the game late in the first with a sprained right ankle. He did not return. ... The Jazz are now 28-3 when they lead entering the fourth, including 12-0 on the road. ... Jazz F Andrei Kirilenko recorded his 600th career steal in the first half.