The Scots need a victory in Salta on Saturday to give themselves a chance of winning the three-match series after losing the opener 28-16 last weekend.
Kinghorn, converted from back-three player to stand-off this season, failed to spark the Scotland attack in the first half in Jujuy but helped create two second-half tries.
Townsend said he was a “massive believer” in the Edinburgh man and had been impressed by the player’s response this week.
“He’s trained well, he’s part of our attack leadership group and has contributed really well in that,” said the coach. “We’re massive believers in Blair in terms of what he can do individually and also how he can lead our team.
“Blair has been very consistent for Edinburgh this year. Very consistent. While he would have wanted to play better last week, it’s all part of the learning and growing experience and process that we have as players, especially the players who have to make a lot of decisions.”
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Townsend has made five changes to his starting XV for the second Test but only one in the backs where scrum-half Ben White comes in for Ali Price for his start for Scotland.
Watson replaces Luke Crosbie at openside flanker and will have Rory Darge alongside him in the back row. The Glasgow Warriors man is preferred to Magnus Bradbury and will wear the No 6 jersey but is more accustomed to playing openside. Watson and Darge played together in the final two matches of the Six Nations, against Italy and Ireland.
Dave Cherry replaces George Turner at hooker and Sam Skinner is picked at lock ahead of Jonny Gray.
London Irish winger Kyle Rowe is in line for his Scotland debut after being named among the replacements. He will be joined on the bench by Jamie Bhatti who takes over from Rory Sutherland as loosehead cover, lock Scott Cummings and back-rower Andy Christie.
Scotland (v Argentina, Estadio Padre Ernesto Martearena, Salta, Saturday, 8.10pm BST)
15. Rory Hutchinson – Northampton Saints – 6 caps
14. Darcy Graham – Edinburgh – 28 caps
13. Mark Bennett – Edinburgh – 25 caps
12. Sam Johnson – Glasgow Warriors – 25 caps
11. Duhan van der Merwe – Worcester Warriors – 17 caps
10. Blair Kinghorn – Edinburgh – 32 caps
9. Ben White – London Irish – 5 chaps
1. Pierre Schoeman – Edinburgh – 10 caps
2. Dave Cherry – Edinburgh – 5 caps
3. Zander Fagerson – Glasgow Warriors – 48 caps
4. Sam Skinner – Edinburgh – 21 caps
5. Grant Gilchrist – Edinburgh – (captain) – 54 caps
6. Rory Darge – Glasgow Warriors – 5 caps
7. Hamish Watson – Edinburgh (vice-captain) – 49 caps
8. Matt Fagerson – Glasgow Warriors – 22 caps
16. George Turner – Glasgow Warriors – 26 caps
17. Jamie Bhatti – Glasgow Warriors – 22 caps
18. Javan Sebastian – Scarlets – 2 caps
19. Scott Cummings – Glasgow Warriors – 21 caps
20. Andy Christie – Saracens – 1 cap
21. Ali Price – Glasgow Warriors – 52 caps
22. Ross Thompson – Glasgow Warriors – 1 cap
23. Kyle Rowe – London Irish – uncapped