Conor Murray will start at scrum-half in Cape Town on Saturday despite Price’s impressive performance in the 22-17 victory in the first Test.
It is one of three changes head coach Gatland has made to his starting XV.
Price’s Scotland team-mate Rory Sutherland is also among the substitutes, with Mako Vunipola replacing him as the starting loosehead prop.
The third change sees Scotland outside centre Chris Harris start the match at outside centre instead of Elliot Daly.
Stuart Hogg and Duhan van der Merwe retain their places at full-back and on the left wing respectively.
Hamish Watson who came off the bench in the second half last Saturday, is not named in the match-day 23.
The Lions will win the three-game Test series if they can beat South Africa this weekend.
“As always, selection was incredibly tough,” said Gatland. “However, we’ve made the changes we think are the right calls for the weekend’s game.
“It’ll be another tight contest. We know the Springboks will be hurting and they’ll throw everything at us on Saturday, but I think there’s plenty more to come from us too. We feel we can go up another level from where we were in the first Test and I would expect us to improve.
“It’s the biggest game on the Tour and we have to embrace the expectation that comes with it. As players and coaches, these are the games you want to be involved in. We’re relishing the opportunity to face the Springboks again on Saturday and potentially seal a Series win.”
Dan Biggar will play at fly-half subject to completing the return-to-play protocol and assessment by an independent concussion consultant after suffering a head knock in the first Test.
Alun Wyn Jones once again leads the side in what will be his 11th successive Lions Test cap, packing down alongside last Saturday’s man of the match Maro Itoje.
Historically, the Lions have lost just two series after winning the first Test - against New Zealand in 1930 and Australia in 2001.
British & Irish Lions team (v South Africa, Second Test, Saturday, Cape Town Stadium, 5pm)
15. Stuart Hogg (Exeter Chiefs, Scotland)
14. Anthony Watson (Bath Rugby, England)
13. Chris Harris (Gloucester Rugby, Scotland)
12. Robbie Henshaw (Leinster Rugby, Ireland)
11. Duhan van der Merwe (Worcester Warriors, Scotland)
10. Dan Biggar (Northampton Saints, Wales)
9. Conor Murray (Munster Rugby, Ireland)
1. Mako Vunipola (Saracens, England)
2. Luke Cowan-Dickie (Exeter Chiefs, England)
3. Tadhg Furlong (Leinster Rugby, Ireland)
4. Maro Itoje (Saracens, England)
5. Alun Wyn Jones – captain (Ospreys, Wales)
6. Courtney Lawes (Northampton Saints, England)
7. Tom Curry (Sale Sharks, England)
8. Jack Conan (Leinster Rugby, Ireland)
16. Ken Owens (Scarlets, Wales)
17. Rory Sutherland (Worcester Warriors, Scotland)
18. Kyle Sinckler (Bristol Bears, England)
19. Tadhg Beirne (Munster Rugby, Ireland)
20. Taulupe Faletau (Bath Rugby, Wales)
21. Ali Price (Glasgow Warriors, Scotland)
22. Owen Farrell (Saracens, England)
23. Elliot Daly (Saracens, England)