Hook made his Wales debut last weekend with an impressive showing off the bench which culminated with an injury-time try in the 27-25 defeat in Puerto Madryn.
He replaces Six Nations centre Matthew Watkins who is struggling with a lower back injury though could still take a place among the replacements.
Jenkins said: "Although Matthew Watkins has suffered with a back injury this week, James very much played himself into this team with his performance on Saturday and in training and he deserves this chance to show us what he is capable of.
"We are waiting until Friday to see if Matthew pulls through over the next few days.
"If he does he will be on the bench but we will have to take a view on selection if he does not."
Bennett, meanwhile, will win his 10th cap for Wales after taking over from Llanelli Scarlets hooker Matthew Rees in a pre-planned move.
Newport-Gwent Dragons centre Nathan Brew comes in for Cardiff wing Chris Czekaj on the bench, though Jenkins has largely kept faith with the same group of players who narrowly lost 27-25 to Argentina in Patagonia.
Jenkins explained: "We always had in mind that we would give Huw Bennett and Matthew Rees an opportunity on this tour and use Richard Hibbard as an impact player in both games.
"That was the policy before we came on tour and we're still happy with that.
"Apart from those two changes, and Nathan coming in for Chris on the bench, we have asked this team to maintain the high standards set last week, add an extra dimension to their play and prove they are capable of beating this Argentinian team.
"We know we were not far away from a victory last week and we know the areas in which we have to improve."
Wales team to play Argentina in second Test in Buenos Aires on Saturday:
Byrne (Ospreys); M Jones (Llanelli), J Robinson (Cardiff), Hook (Ospreys), S Williams (Ospreys); N Robinson (Cardiff), Phillips (Cardiff); D Jones (capt, Ospreys), Bennett (Ospreys), A Jones (Ospreys), Gough (Newport Gwent), Evans (Ospreys), AW Jones (Ospreys), G Thomas (Llanelli), Popham (Llanelli)
Replacements: Hibbard (Ospreys), Yapp (Cardiff), R Thomas (Newport Gwent), Delve (Bath), A Williams (Bath), Brew (Newport Gwent), AN Other.