The trio are among 10 additions to Rennie's Nations Championship squad that beat France, Italy and Ireland in a perfect start to the inaugural global tournament.
Tupou Ta'eiloa, a 22-year-old flanker, made a name for himself at Moana Pasifika in the last couple of Super Rugby seasons after being overlooked by New Zealand's established teams.
With Moana Pasifika disbanded due to financial problems at the end of the season in June, Tupou Ta'eiloa is now hot property for his destructive ball-carrying ability.
Wellington Hurricanes' Lauaki will battle fringe props Xavier Numia and Ollie Norris for match minutes, while Otago Highlanders-bound Jacomb joins Ruben Love, Beauden Barrett and Damian McKenzie among Rennie's flyhalf options after a strong final season at Waikato Chiefs.
Former captain and lock Scott Barrett, explosive wing/centre Leicester Fainga'anuku and prop Tamaiti Williams were omitted due to injury.
However, Netherlands-born lock Fabian Holland was recalled after recently returning to action following a long recovery from a shoulder injury.
The other six additions are Norris, hooker George Bell, flanker Ethan Blackadder, midfielder Timoci Tavatavanawai and outside backs Rieko Ioane and Emoni Narawa.
"We're playing the best team in the world. It couldn't come at a better time for us," Rennie told a press conference in Auckland on Monday.
"We're going to be tested against a phenomenal side on their home patch, so it's exciting.
"This would have to be the toughest tour in rugby."
Marketed as "Rugby’s Greatest Rivalry", the tour kicks off in Cape Town on August 7 against provincial side Stormers, with the first test on August 22 at Johannesburg's Ellis Park.
Rennie said 109-test hooker Codie Taylor was the tour captain, with regular skipper Ardie Savea to be rested for matches against provincial sides Stormers, Sharks and Bulls before the first test.
Flyhalf Richie Mo'unga was not included in the squad as he makes his return to New Zealand from a three-year stint in Japan, but Rennie said he could be called up if injuries hit.
World champions South Africa also started the Nations Championship with a perfect 3-0 record after beating England, Scotland and Wales.
New Zealand squad to tour South Africa
Forwards: Asafo Aumua, Codie Taylor, Samisoni Taukei'aho, George Bell, Ethan De Groot, George Bower, Xavier Numia, Ollie Norris, Tyrel Lomax, Fletcher Newell, Pasilio Tosi, Siale Lauaki, Tupou Vaa'i, Patrick Tuipulotu, Josh Lord, Sam Darry, Fabian Holland, Peter Lakai, Simon Parker, Ethan Blackadder, Luke Jacobson, Anton Segner, Ardie Savea (capt), Wallace Sititi, Semisi Tupou Ta'eiloa
Backs: Cameron Roigard, Cortez Ratima, Kyle Preston, Ruben Love, Beauden Barrett, Damian McKenzie, Josh Jacomb, Jordie Barrett, Quinn Tupaea, Billy Proctor, Anton Lienert-Brown, Timoci Tavatavanawai, Caleb Clarke, Fehi Fineanganofo, Leroy Carter, Josh Moorby, Will Jordan, Rieko Ioane, Emoni Narawa
The All Blacks are embarking upon their first full tour of South Africa since 1996! Marketed as the 'Greatest Rivalry' series, the winner will come out not only with the bragging rights but World Rugby's number one ranking. Keep up to date throughout August and September with news, previews and more.
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