It's a very real possibility now, as Argentina need a win away to Ecuador in the high altitude of Quito to qualify, although a draw may get them through if Colombia defeat Peru. La Albiceleste are 6th in the standings, behind Chile, Colombia and Peru - and now face the most daunting of prospects.
Jorge Sampaoli's men toiled away for most of the night, with Messi creating more than his fair share of chances, but the finishing touch simply deserted his teammates. Peru's defensive organization was downright heroic at times, and they deserved this result.
That's it from us tonight - thank you for following the game with us, and do check back for Argentina's pivotal clash against Ecuador.
90+4' Unselfishly, Messi goes for a chip to the far post, but Gallese comes out and claims the ball with ease. Moments later, Acuna concedes a foul on the edge of his own box, and Peru have a chance now! Guerrero to take...
90+1' SHOT BLOCKED YET AGAIN! Messi finds space on the edge of the box, and lets fly, but his effort is blocked by Araujo yet again. What a defensive performance he's had.
89' INTO THE WALL! Messi sends his free-kick straight into the wall. Moments later Acuna goes into the book for dissent, as the referee awards a foul in favour of Peru.
88' What a mistake! Messi is crudely chopped down on the edge of the box. A free-kick in Messi territory. Can he do it?
87' Messi clips a ball over the top to Benedetto, but the ball is slightly too overhit. Moments earlier, Andy Polo had run clear for Peru, but was offside only by inches!
83' After a bit of head-tennis in the box, Argentina eventually manage to clear the ball. The home side launch a long ball to Papu Gomez, but the ball goes out for a goal kick.
81' Mascherano, who seems to be back to normal, chips a ball forward to Messi making a run into the box, but Gallese is alert and punches clear. Moot, as Messi was offside.
77' WELL THAT WOULD HAVE BEEN AMAZING! Of all the people in the world, Javier Mascherano lets fly from range, with his effort going inches over the bar!
74' The visitors attempt to release the pressure with a rare foray forward, but a long ball to Guerrero is easily collected by Sergio Romero.
Moments later, Papu Gomez performs an awful dive in the box after realizing he cannot reach a cross from the right. The ref isn't conned, and play continues.
72' Peru are falling back deeper and deeper. They're inviting pressure from Argentina who are reduced to aimless crosses after passing it from side to side.
68' YET ANOTHER SAVE FROM GALLESE! Stunningly, Messi finds himself in space in the middle as Argentina counter-attack and he sends Benedetto clear down the left, but his low drive is straight at the Peruvian keeper, attempting to nutmeg him, but Gallese makes the save with his legs.
He celebrates moments later by taking his time over a goal-kick.
61' ANOTHER VITAL TOUCH FROM TRAUCO! Messi makes a mesmerizing run down the left wing, before sending in a low cross to the near post that is simply begging to be tapped home. Rigoni looks to have done so, but Trauco slides in at the last moment to deny the goal-bound shot from getting into the net!
57' ANOTHER HUGE SAVE FROM GALLESE! Lovely football from Messi as he exchanges passes with Banega down the middle, before a through ball sends Papu Gomez clear on the left side of the box, but Gallese is alert to deny his powerful shot at the near post!
50' The referee has words with Guerrero and Otamendi yet again, as the pair have another argument following a heavy challenge by the Peruvian legend this time.
47' SAAAVE! Biglia hammers a shot from range and forces Gallese into a full stretch save, with the Peruvian keeper managing to get hurt in the process. A bit of treatment, and he's back up.
46' OFF THE POST! SO SO UNLUCKY! Messi sends Benedetto clear down the right channel and he forces Gallese into a save, but the ball falls to Messi rushing into the box with his shot taking a deflection off Trauco's boot and agonizingly clanging off the post and out.
45' OOOOH! WHAT A CHANCE! Messi collects the ball on the left channel, and sends in a beautiful cross to Benedetto making a run to the far post and the Boca Juniors striker loops his header over the bar instead of burying it downward and into the net!
42' Another misplaced pass from Benedetto, and his own fans at the Bombanera, let out agonized groans. This is getting rather painful to watch, as the home side look bereft of ideas.
38' MESSSIIII! SO CLOSE! With the most exquisite of shoulder drops, Messi gets away from his marker in the middle and drives his way to the left edge of the box, before unleashing an effort that flies inches wide of the post. There was a deflection, and Argentina are awarded a corner, but nothing comes of it.
33' FINALLY! Papu Gomez turns his marker inside and out from the left, before a quick snapshot forces Gallese into making a nearpost save. The first of this rather dreary match! Argentina can't make anything from the set piece though.
29' Sampaoli is absolutely livid on the touchline after Benedetto misplaces a pass under no pressure, bringing an end to a promising attack down the left.
28' Messi is dispossessed twice in quick succession - he's not making the best of impressions in his first ever official appearance at La Bombanera. Meanwhile, Nico Otamendi is lucky to escape a yellow card after a late challenge on Guerrero.
26' There's plenty of rough stuff from Peru in the middle, with Sergio Pena the latest to give away a foul, in what is quickly becoming a stop-start affair.
24' SUPERB DEFENDING! Messi shows great strength to hold off his marker and burst down the middle, laying the ball off for Benedetto to run clear into the box, but Araujo slides in with a last-ditch tackle. The ball rebounds to Di Maria, who shoots from distance, but his effort is ... pathetic, to say the least.
23' Midway through the first half, and the first groan of the night is heard, as Mercado sends a cross from the right into the stands, when under no pressure at all.