Despite their dominance, Gerardo Martino's men looked set to have to settle for a single-goal victory thanks to Nestor Renderos' own goal after 54 minutes, but substitute Mancuello fired home a free-kick from an acute angle with two minutes left to steal the headlines.
For all their possession, Argentina rarely impressed before the break, producing a laboured and largely toothless display.
They improved in the second half, though, and shortly after Carlos Tevez had fired an effort just wide, Ever Banega found the net from distance with a little help from Renderos' deflection.
El Salvador, ranked 87 places below Argentina in the FIFA world rankings, offered little from an attacking perspective and had to rely on goalkeeper Derby Carrillo to keep the score down.
Carrillo continued to catch the eye in the final stages, but he was ultimately beaten in spectacular fashion with time running out, as Independiente ace Mancuello stepped off the bench to make an almost immediate impact on the international stage.
Despite Lionel Messi's omission from the starting XI due to a reported foot knock, Argentina looked purposeful during the early exchanges and they should have broken the deadlock as early as the third minute.
Mateo Musacchio met Ezequiel Lavezzi's right-wing delivery at the near post, flicking it to the far side of the goal for what appeared to be a simple chance for Gonzalo Higuain, who headed wide of the unguarded net.
Argentina struggled to build upon that early promise, though, as El Salvador's defensive tactics allowed little room for manoeuvre in the final third for Martino's attackers.
Higuain did eventually force El Salvador goalkeeper Carrillo into action in the 29th minute, cutting in from the left and seeing his powerful drive palmed away.
Carrillo was tested again five minutes before the break but this time he comfortably turned Angel Di Maria's free-kick around the post.
Argentina looked a little more fluid once again after the break and Tevez went close to breaking the deadlock in the 52th minute, but his 20-yard effort was deflected agonisingly wide.
Luck went Argentina's way just a few moments later, however, as Banega's hopeful long-range effort struck Renderos and flew past the helpless Carrillo to give the FIFA World Cup finalists the lead.
It would have been 2-0 shortly afterwards if not for Carrillo, who acrobatically tipped a Tevez attempt over the crossbar.
Carrillo looked set to keep the score down as he denied Tevez again 18 minutes from time, but he was rendered helpless two minutes from the end.
Mancuello, who replaced Di Maria with 17 minutes left, stepped up to curl a free-kick out towards the corner flag and his looping delivery dropped into the far corner, capping a memorable day for the midfielder.
