The City forward was a half-time substitute for Lautaro Martinez who had earlier opened the scoring on 16 minutes.
Lionel Messi added another from the penalty spot in first half stoppage time.
Alvarez, winning a 10th cap for his country, was quickly into the action, with clever movement and pressing but it was Messi who increased Argentina’s lead with a delightful chip on 69 minutes.
Alvarez almost claimed an assist as he set up Enzo Fernandez who saw his long range effort hit the post on 82 minutes.
International round-up
Elsewhere, it was a largely disappointing night for our players.
Seven City stars were in action on Friday evening, with only Ederson’s Brazil and Riyad Mahrez‘s Algeria recording victories – though City keeper Ederson was watching from the bench.
With both England and Germany losing their Nations League games and Algeria edging a narrow win over Guinea, friendly, it was mostly an evening to forget.
England
England’s woeful Nations League campaign continued as Gareth Southgate’s men were beaten 1-0 by Roberto Mancini’s Italy.
Phil Foden and Kyle Walker both started for England, but it was a mostly toothless display by the Three Lions who have shown some worrying form ahead of the World Cup later this year.
Giacomo Raspadori’’s stunning strike for the hosts on 68 minutes would prove to be the only goal of a game that rarely lived up to expectations.
Jack Grealish was introduced for Bukayo Saka on 72 minutes in what was a double substitution that saw Walker replaced by Luke Shaw.
As ever, Grealish was on the end of a number of enthusiastic challenges during the time he was on the pitch – though the City winger picked up a yellow card himself in added time - as the Azzurri held on for a victory that means England are relegated to the Nations League B.
Foden played the full 90 minutes.
On Saturday afternoon, Rico Lewis played 51 minutes of England U19s’ 6-0 win over Georgia at the Hjørring Stadium, Denmark in a U19s European Championship qualifier.
Germany
Ilkay Gundogan’s Germany were the latest team to suffer at the hands of an ever-improving Hungary team.
The Germans fell behind to a Ádám Szalai goal after 17 minutes of the Nations League clash in Leipzig.
Gundogan was replaced on 69 minutes as Germany fell to third in Group I with one game remaining.
Algeria
Riyad Mahrez started on the bench as Algeria took in Guinea in a friendly.
The City winger came on after 67 minutes in an effort to unlock a resolute Guinea defence.
And his introduction paid dividends when Mahrez assisted Islam Slimani’s 79th-minute winner.
Brazil
Ederson was an unused sub as Brazil beat Ghana 3-0 in Le Harve, France.
Goals from Marquinhos (9 minutes) and Richarlison 28 and 40 minutes) eased the Seleção to a comfortable friendly victory.
