The striker, one of six City stars at the prestigious competition, started the second straight match for Javier Mascherano’s Under-23s as one of three ‘overage’ players.
It was the perfect response to La Arana’s nation’s 2-1 defeat to Morocco last time out as they collected three points and boosted their chances of reaching the knockout phase.
And Argentina will be aiming to secure passage to the quarter-finals in their final group assignment, a meeting with Ukraine on Tuesday 30 July.
Following slightly cagey opening exchanges, Alvarez was at the heart of the game’s first goal when he squared the ball to Thiago Almada who coolly converted into the bottom corner.
City’s forward continued to be a thorn in his opponents’ side and he looked to double Mascherano’s men’s lead when drove towards the box but was thwarted by a good challenge by an Iraq defender.
Looking to bounce back from their defeat to Morocco in the previous match, the South American side pushed for a second and it almost arrived when Almada cut inside and whipped a vicious attempt just wide.
However, Iraq – who beat Ukraine 2-1 in their opening Olympics match – proved they still packed quality aplenty when they equalised on the cusp of half-time through Aymen Hussein’s close range header.
In what was shaping up to be another exciting contest at the Paris games, Argentina restored their lead 20 minutes after the interval when Luciano Gondou met a pinpoint cross to nod the ball into the net.
After playing five of his nation’s six games en route to Copa America glory earlier in July, Alvarez was again crucial at the Olympic Games when he provided another assist - this time for Ezequiel Fernandez’s sublime lob to extend their advantage further.
That proved to be the game’s last goal as Alvarez and Co. collected three vital points ahead of their group stage decider against Ukraine on Tuesday 30 July at 16:00 (UK).
