City’s exciting attacker led the line for the reigning world champions and played 80 minutes at La Bombonera, but goals from Ronald Araujo and Darwin Nunez inflicted defeat on Lionel Scaloni’s side.
After even opening exchanges, the Barcelona defender opened the scoring by ghosting in at the far post and coolly slotting home to send the away support wild in Buenos Airies.
Lionel Messi came close to equalising for the hosts when his clipped free-kick hit the bar early in the second half.
However, it would be Marcelo Bielsa’s side’s night when they sparked a clinical counter attack late on which allowed Nunez to drive into the box and fire past Emi Martinez.
Despite tasting defeat for the first time in qualifying, Argentina remain top of South America’s group on 12 points.
Elsewhere, Ederson was an unused substitute as Brazil also lost in World Cup qualifying after suffering a 2-1 defeat to Colombia.
Arsenal’s Gabriel Martinelli broke the deadlock after just four minutes at Estadio Metropolitano.
A second-half brace, though, from Liverpool’s Luis Diaz was enough for the hosts to flip the match on its head and collect three points.
Tite’s side sit fifth in the qualifying table as a result on seven points after a record so far of two wins, one draw and two losses.
Argentina and Brazil’s next fixture could see Alvarez and Ederson lock horns when the two nations meet at the Maracana on Wednesday 22 November at 00:30 (UK).
