The Pumas went down 23-26 to England in the Bronze Final at Stade de France.
England claimed third place at the Rugby World Cup for the first time after an entertaining, if stop-start, 26-23 victory over Argentina at Stade de France.
Either side of two Owen Farrell penalties, a lovely delayed pass by Marcus Smith put Ben Earl through a gap to score the opening try on nine minutes, which Farrell converted.
The teams exchanged penalty goals before Argentina finally got a proper foothold in the game three minutes before half-time, scrum-half Tomas Cubelli diving over the tryline from close range after Los Pumas stretched the England defence on both wings. Emiliano Boffelli converted.
Santiago Carreras's brilliant solo effort put Argentina in front early in the second half but England hit back straight away, Theo Dan gathering his charge-down of Carreras's kick to score England's second try. This left Farrell (pictured right), with a perfect display from the kicking tee, to see his team home.
England flanker Sam Underhill was named Mastercard Player of the Match after making 24 tackles. "It is a bit surreal," he said, having been called up to the squad as an injury replacement.
"We just stuck to our gameplan, we didn't panic. A lot of the lads know it is the last 20 minutes of these games that matter and that is testament to them."
"We started the game really well, but it was pretty scrappy thereafter," England captain Owen Farrell said. "We did what we needed to do to grind out a win.
"Last week we didn't quite get it done but we wanted to finish off this tournament right.
"We feel like we have got better and better and built through the tournament. There is a lot to come for this team."
England head coach Steve Borthwick admitted it "wasn't a game of high quality but one of high tension" then paid tribute to man-of-the-moment Underhill.
"To miss out [on the original squad] and then come in and train the way he has and play the way he did tonight, he deserves enormous respect."
Argentina captain Julian Montoya rued his team's lack of consistency: "We made some mistakes, we need to be better at controlling things. We scored a try but then we conceded points straight after from their kick-off."
"It was fine margins," head coach Michael Cheika agreed. "We didn't get the rub of the green on many things but we still stayed in the game.
"We've had a good campaign ... but I am disappointed with the way the game was refereed.
"I think we deserved to win tonight and for one reason or another we didn't."
Argentina 23 [Tries: Cubelli, S. Carreras; Cons: Boffelli 2; Pens: Boffelli 3] England 26 [Tries: Earl, Dan; Cons: Farrell 2; Pens: Farrell 4]
Argentina: 15 Juan Cruz Mallia, 14 Emiliano Boffelli, 13 Lucio Cinti, 12 Jeronimo de la Fuente, 11 Mateo Carreras, 10 Santiago Carreras, 9 Tomas Cubelli, 8 Facundo Isa, 7 Marcos Kremer, 6 Juan Martin Gonzalez, 5 Pedro Rubiolo, 4 Guido Petti, 3 Francisco Gomez Kodela, 2 Julian Montoya (captain), 1 Thomas Gallo.
Replacements: 16 Agustin Creevy, 17 Joel Sclavi, 18 Eduardo Bello, 19 Matias Alemanno, 20 Rodrigo Bruno, 21 Lautaro Bazan Velez, 22 Nicholas Sanchez, 23 Matias Moroni.
England: 15 Marcus Smith, 14 Freddie Steward, 13 Joe Marchant, 12 Manu Tuilagi, 11 Henry Arundell, 10 Owen Farrell (captain), 9 Ben Youngs, 8 Ben Earl, 7 Sam Underhill, 6 Tom Curry, 5 Ollie Chessum, 4 Maro Itoje, 3 Will Stuart, 2 Theo Dan, 1 Ellis Genge
Replacements: 16 Jamie George, 17 Bevan Rodd, 18 Dan Cole, 19 David Ribbans, 20 Lewis Ludlam, 21 Alex Mitchell, 22 George Ford, 23 Ollie Lawrence
Referee: Nic Berry (Australia)
Assistant Referees: Nika Amashukeli (England), Andrew Brace (Ireland)
TMO: Ben Whitehouse (Wales)