Floyd Pinto's side had lost against Murcia U-20 (2-0) and Mauritania U-20 (3-0) and held Venezuela U-20 to a goalless draw in their previous engagements of the COTIF international football and will take a lot of heart in the win over the record six-time U-20 World Cup champions.
Deepak Tangri (4') scored early for India before Aniket Jadhav was sent off in the 50th minute, after which Anwar Ali (68') doubled the lead before Argentina pulled one back in the 72nd minute.
The Indians couldn't have asked for a better start as Tangri headed the ball at the back of the net from a corner taken by Ninthoiganba Meetei in the fourth minute.
Pumped by the lead, the Asian outfit kept attacking and did fairly well in the midfield to create a couple of more opportunities in the first half. Jadhav was the intended target in the moves initiated by Suresh Singh Wangjam and Boris Singh Thangjam but was short on reaching the pass and was adjudged off-side in the two chances.
At the back, Anwar Ali was standing tall while Meetei, who provided the assist for the opener, was up to the task as well.
In the second half, Ali had an opportunity after receiving a pass from captain Amarjit Singh Kiyam but his attempt was saved by the Argentine goalkeeper.
Just when it was looking promising, Jadhav was shown the red card and the India U-20 side were reduced to 10 men in the 54th minute.
Pinto's boys contained themselves despite the South Americans attacking in numbers with goalkeeper Prabhsukhan Gill needing to pull off a save in the 56th minute and another with his fingertips in the 61st minute.
Fortune favoured the brave as India took the lead through a brilliantly struck free-kick taken by Anwar Ali in the 68th that hit the inside of the woodwork before nestling in the Argentine goal. The set-piece was a result on a foul on substitute Rahim Ali, who had replaced Meetei at half-time.
However, it was not going to be a clean sheet for Gill as his goal was breached in the 72nd minute.
India held on to their nerves to safeguard their one-goal lead and were lucky that an Argentine attempt late into the five-minute injury time came off the crossbar.
India U-20's starting XI: Prabhsukhan Gill (GK), Asish Rai, Jitendra Singh, Anwar Ali, Sahil Panwar, Boris Singh Thangjam, Suresh Singh Wangjam, Deepak Tangri, Amarjit Singh Kiyam (C), Ninthoinanba Meetei, Aniket Jadhav.