Substitute Joaquin Correa added a fifth after the break, completing a commanding result for the Qatar-bound visitors, in front of a 36,000 capacity crowd.
Alvarez opened Argentina's account in the 17th minute, finishing off a Messi low cross, smoothly flicking the ball past UAE 'keeper Khalid Eisa.
A first-time volley from Di Maria off a brilliant Marcos Acuna cross found the far corner to double Argentina's lead in the 26th minute.
Messi almost got on the board with a signature free kick that just cleared the bar but the visitors did not need to wait long for another goal as Di Maria connected with an Alexis Mac Allister pass and dribbled his way past the entire UAE defence to make it 3-0 for La Albiceleste inside 36 minutes.
A Messi header just before the break was saved by Eisa but the former Barcelona star was not to be denied as he and Di Maria wreaked havoc on the edge of the box before Messi sprinted through down the right and fired past the UAE 'keeper.
Substitute Correa extended Argentina's lead in the 60th minute, latching onto a Rodrigo de Paul through pass for goal number five.
UAE's Caio Canedo almost struck back immediately but his close-range strike sailed over the bar. Another opportunity came via Abdulaziz Heikal, who sent a dangerous cross into the box but Canedo's effort went just wide.
Messi curled a free kick in the 78th minute that was a few inches wide before Canedo missed twice from close range.
Argentina will now fly to Doha where they kick off their World Cup campaign against Saudi Arabia on 22 November at Lusail Stadium.