Read more: FIFA World Cup 2022 Qatar: Quarter-Final results
After Man City striker Alvarez earned a debatable penalty following a collision with Croatia goalkeeper Dominik Livakovic, Messi fired into the top corner from the penalty spot in the 34th minute to open the scoring.
Lionel Messi surpassed Gabriel Batistuta to become Argentina's top scorer at World Cup finals on 11 goals after scoring from the spot.
Croatia collapsed after the opener and conceded another five minutes later from an Argentina counter-attack after shaky defending as Alvarez doubled their lead in the 39th minute, carried the ball from his own half.
Messi took matters into his own hands to ensure the game was out of reach, producing a moment of magic down the right to beat Josko Gvardiol before putting it on a plate for Alvarez to score Argentina's third.
Argentina last reached the World Cup final in 2014 in Brazil and were beaten by Germany, but have not lifted the trophy since Diego Maradona led his nation to victory in Mexico in 1986.
The second semi-final between France and Morocco will be played tonight, 14th December at the Al Bayt Stadium.