Elias and Francis will get their first starts of the tour as they join Rob Evans in a new-look front row while Jenkins is part of a highly competitive back row that also features James Davies and Ross Moriarty.
Watkin replaces injured centre Hadleigh Parkes while prop Samson Lee misses out due to a back injury.
Wales are in prime position to win all three of their tour matches having edged out South Africa in the first test before beating Argentina for the first time in 14 years.
"We want to go home three from three but we know the challenge that we are up against this weekend and we also are looking at the bigger picture," Gatland told reporters.
"We might have picked a slightly different team if it was just about results but it is about more than that it is about building for 2019 and we are on the right track."
The final test of the tour will be played at the Estadio Brigadier Lopez in Santa Fe.
Wales team:
15-Hallam Amos, 14-Josh Adams, 13-Scott Williams, 12-Owen Watkin, 11-George North, 10-Rhys Patchell, 9-Aled Davies, 1-Rob Evans, 2-Ryan Elias, 3-Tomas Francis, 4-Adam Beard, 5-Cory Hill(captain), 6-Ellis Jenkins, 7-James Davies, 8-Ross Moriarty
Replacements:
16-Elliot Dee, 17-Nicky Smith, 18-Dillon Lewis, 19-Bradley Davies, 20-Josh Turnbull, 21-Tomos Williams, 22-Gareth Anscombe, 23-Tom Prydie
(Reporting by Aditi Prakash in Bengaluru; Editing by Toby Davis)
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