Lions head coach Warren Gatland has made six changes to the side that lost 27-9 in last weekend's encounter in Cape Town.
Hooker Ken Owens, prop Wyn Jones, scrum-half Ali Price, centre Bundee Aki, wing Josh Adams and full-back Liam Williams all come into the XV.
Wales duo Adams and Williams are likely to have an important role in the back three under the Springboks' kicking game that dismantled the Lions after half-time last time out.
Tight-head prop Sinckler will take his place on the bench alongside fly-half Finn Russell, lock Adam Beard and number eight Sam Simmonds – the three of whom are in Test squad for the first time in the series.
Gatland has axed Owen Farrell Taulupe Faletau, Anthony Watson, Stuart Hogg, Rory Sutherland, Tadhg Beirne and Chris Harris from his 23.
"The matchday 23 have an incredibly special opportunity in front of them - to seal a Lions series victory in South Africa," said the veteran coach.
"It doesn't get much bigger than this and we're excited by the challenge that faces us on Saturday.
"We've no excuses from last week - the Springboks put us under pressure in the second half and deserved the win. We have to be much better than that second-half performance, and I believe we will be."
Sinckler denied allegations that he bit Franco Mostert and World Rugby were unable to find sufficient evidence to punish the England forward, who was facing a minimum 12-week ban.
A statement from the governing body read: "Having reviewed all the evidence, the committee deemed that on the balance of probabilities, it could not be satisfied that the player committed an act of foul play.
"On that basis, the committee dismissed the citing and the player is free to play again immediately."
South Africa are without world player of the year Pieter-Steph du Toit and influential scrum-half Faf de Klerk through injury.
Cobus Reinach comes in for De Klerk while Franco Mostert's switch to blindside flanker means Lood de Jager will partner Eben Etzebeth in the second row.
Veteran fly-half Morne Steyn, whose long-range penalty secured a series triumph for the Springboks over the Lions in 2009, is named on the bench.
British and Irish Lions: Liam Williams, Josh Adams, Robbie Henshaw, Bundee Aki, Duhan van der Merwe, Dan Biggar, Ali Price; Wyn Jones, Ken Owens, Tadhg Furlong, Maro Itoje, Alun Wyn Jones (captain), Courtney Lawes, Tom Curry, Jack Conan
Replacements: Luke Cowan-Dickie, Mako Vunipola, Kyle Sinckler, Adam Beard, Sam Simmonds, Conor Murray, Finn Russell, Elliot Daly
South Africa : Wille le Roux, Cheslin Kolbe, Lukhanyo Am, Damian de Allende, Makazole Mapimpi; Handre Pollard, Cobus Reinach; Steven Kitshoff, Bongi Mbonambi, Frans Malherbe, Eben Etzebeth, Lood de Jager, Siya Kolisi (captain), Franco Mostert, Jasper Wiese
Replacements: Malcolm Marx, Trevor Nyakane, Vincent Koch, Marco van Staden, Kwagga Smith, Herschel Jantjies, Morne Steyn, Damian Willemse