The Red Rose, without as many as 30 players due to injuries and other commitments, trailed 31-23 at one point and looked to be heading for back-to-back defeats for the first time under their boss.
Rugby league convert Denny Solomona, one of 10 new caps in the England ranks, scored on his debut in the final minute to complete an impressive turnaround, however, leaving Jones full of pride come full time.
"I thought it was an incredible game of rugby," he is quoted as saying by Sky Sports News. "I thought for our guys to win that was a tremendous effort. In the end, I think we had 10 new caps out there and to show poise and stick to what we needed to do in the circumstances was an unbelievable effort from the young guys.
"When you are playing a full-strength Argentina team, I think it is one of the best team efforts I have been associated with. George Ford was absolutely brilliant. There were guys who made mistakes but they didn't dwell on them.
"Denny made two horrendous errors in defence but got one back. He is going to be doing some defensive work next week. If you see him tackling tackle bags in the streets of Buenos Aires you know why."
Ford registered 23 of England's 38 points, crossing over once and converting from seven of his eight kicks.