After losing to Colombia and drawing with Paraguay in their first two matches, La Albiceleste required victory to secure a spot in the last eight.
Lionel Messi and Martinez fired over in the space of a minute early on, but the latter made no mistake when the only big chance of the first half fell his way four minutes in.
La Albiceleste struggled to create much beyond that point in the opening 45 minutes, however, with Aguero - restored to the side today - scuffing wide from a good position and Martinez seeing a goal-bound shot blocked on the line.
The man at fault for Argentina's opener nearly levelled before half time as Al Rawi's free kick curled around the wall but clipped the outside of the post.
Aguero twice came close in the space of a couple of minutes with an hour played as he was denied by a block from Karim Boudiaf and then by some good goalkeeping from Al Sheeb.
The Manchester City striker was much more involved in the second half of the match and he felt he should have had a penalty 72 minutes in when pulled down by Boualem Khoukhi in the box.
A promising chance then came and went for Messi, who picked out the stands with his shot from right on the penalty spot, but Argentina finally put the game out of reach eight minutes from time.
Aguero was the man to score it after getting away from a couple of players and firing the ball across Al Sheeb to kickstart his side's campaign.
QATAR (3-5-2): Al Sheeb; Al Rawi, Khoukhi, Salman; Miguel (Ismaeil 85'), Al Haydos, Al Hajri (Al Ahrak 77'), Hatim, Boudiaf; Afif, Ali
ARGENTINA (4-3-3): Armani; Saravia, Foyth (Pezzella 85'), Otamendi, Tagliafico; De Paul, Paredes, Lo Celso (Acuna 55'); Messi, Martinez (Dybala 76'), Aguero