Enyeama quit the team in 2015 after falling out with then head coach Sunday Oliseh but there have been loud calls for him to return for next year's World Cup.
Nigeria's senior team have played Argentina eight times since 1994 and Tuesday's victory is only the second time the Eagles are coming out on top.
Nigeria's Super Eagles on Tuesday evening came back from two goals down to overcome a Messi-less Argentina 4-2 in Russian Federation.
The player has since returned to the team hotel with the rest of the squad.
Sevilla star Ever Banega had beaten a poorly positioned Daniel Akpeyi in goal for Nigeria and who didn't arrange his wall properly in the 14th minute to give Argentina the lead.
On resumption for the second half, Eagles up their game with skipper John Mikel Obi who was playing his 80th worldwide game at the senior level for Nigeria spraying accurate passes.
Kelechi Iheanacho's brilliant first half free kick halved the deficit before a second half brace from Arsenal's Alex Iwobi and a debut goal from Bryan Idowu ensured victory for the Eagles.
Abdullahi ( 5/10) - Like Awaziem, he also had an average performance. Just as Algeria coach, Rabah Madjer pointed him out as the most lethal in the Eagles forward line, the Arsenal player scored two lovely goals and was constantly a threat to the Argentines each time he had the ball in his legs.