Both suffered series-ending injuries on Saturday as the world champion Springboks beat the All Blacks 29-24 in Soweto and grabbed a 2-1 lead in the four-Test series.
Kolbe, South Africa's flawless goalkicker in the series, broke his jaw when he was run over by Luke Jacobson, and Savea, the All Blacks captain, copped a suspected dislocated right shoulder in a clearout by Jasper Wiese after 30 minutes.
Also New Zealand centre Quinn Tupaea damaged his MCL.
Neither team planned to replace them in the squad for the final match next Saturday at the NFL home of the Baltimore Ravens.
South Africa imposed their forward power as, for the first time in the series, they matched New Zealand for tries - four each - and Sacha Feinberg-Mngomezulu replaced injured goalkicker Cheslin Kolbe to slot seven points.
Crucially, counterpart Ruben Love missed seven out of a possible nine points off the tee.
Having guided the Springboks into a series lead after losing the first match, coach Rassie Erasmus was relieved.
"It was epic, it was intense," he said. "We're just happy we won."
He believed the main difference between the sides was the depth of team knowledge between him and New Zealand counterpart Dave Rennie. Erasmus has had oversight of the Boks since 2018 and Rennie since June.
"Dave doesn't have that luxury yet," Erasmus said. "He's building a team and I know what that feels like; in 2018 I got the team 18 months before a World Cup.
"I know these players inside out. They know me. We've got the luxury of knowing each other for nine years, through tough times, and that's not to say we're always going to win because of that, but we're just a little more used to (tough times).
Erasmus believed the score fairly reflected the contest. The Springboks didn't lead the third Test until the game was an hour old and fought hard for an edge in the set-pieces.
"We're not sitting here thinking we are awesome," he said. "We're thinking there was also a lot of luck that went our way."
Rennie believed the gap between the teams was small and thought a couple of errors on Saturday made the difference.
"It's frustrating because there was a lot of effort out there but we just weren't clinical in that first half and couldn't wrestle momentum back when it mattered in that second half," he said.
The first key moment in the second half was when New Zealand scored to lead 17-12 and immediately gave it away when winger Leroy Carter fell off South Africa centre Jesse Kriel, who scored.
"I feel for Leroy. He's a good man, he's a very good defender, I'm sure he's hurting about that," Rennie said.
The second moment was Will Jordan kicking the ball dead.
"Just unlucky," Rennie said. "It was a good option but you come back to a scrum, which is a penalty, which is a maul where they drive however many metres to score."
That maul try to hooker Malcolm Marx was the killer blow.
"We scrambled to try and get in front of it and they kept rolling through us," Rennie said. "It was the only (maul) that troubled us today. It's disappointing."
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