Alejandro Sabella's men were comfortable throughout Saturday's encounter in Buenos Aeries, and will head to Brazil for the FIFA World Cup on the back of consecutive friendly victories, having defeated Trinidad and Tobago 3-0 on Wednesday.
Argentina made a measured start and took the lead with the first meaningful effort as Alvarez's well-placed strike beat Vid Belec in the Slovenia goal.
Maxi Rodriguez spurned a great chance for a second before the break with a tame effort, while the same man was denied by a superb save from Belec.
However, Sabella introduced Sergio Aguero, Angel di Maria and Messi in the second half, and it was the Barcelona man who ensured the comfortable win with a neat finish inside the area.
Argentina can now look forward to their Group F opener with World Cup debutants Bosnia-Herzegovina on June 15.
The hosts had claims for a penalty as early as the 10th minute when Ezequiel Lavezzi tumbled in the area under Dalibor Stevanovic's challenge, but referee Martin Vazquez deemed that the midfielder had won the ball.
Argentina had the lead two minutes later, however, Alvarez opening his international account with a low left-foot drive from 20 yards that accurately found the bottom right-hand corner.
Shortly after, Lucas Biglia took a knock to his knee and was replaced by Hugo Campagnaro, seemingly as a precaution.
The change did little to disrupt Argentina and Rodriguez should have doubled the ahead when he collected Javier Mascherano's pin-point throughball in the area, only to shoot tamely at Belec when one-on-one.
Rodriguez was at the heart of the action again in the 35th minute, his superb curling effort from the edge of the box drew a great save from Belec, who tipped the ball onto the bar.
Argentina continued the pressure after the break and Alvarez could have had a second, only for Belec to deny his Inter colleague after neat work from Lavezzi.
With the tempo slowing, Sabella introduced Messi, Di Maria and Aguero into the action, yet it was Slovenia who went close to an undeserved equaliser when Milivoje Novakovic spun well in the box but shot straight at Sergio Romero.
That was as good as it got for the visitors, however, and Argentina saw Di Maria scuff an effort wide before Aguero squared a superb ball across the six-yard box but his team-mates failed to gamble on the delivery.
However, the second did arrive for Argentina in the 76th minute when Aguero's knockdown Di Maria's cross was stabbed home by Messi.
The goal was Messi's first for his country in 2014 and will give him a fillip as he looks to lead Argentina to glory in rival territory in the coming weeks.
