The Inter striker capped a box-to-box move, knocking down a long ball from keeper Geronimo Rulli to Erik Lamela, who returned the pass for Icardi to score.
It was the 25-year-old's first goal for Argentina in his eighth game for his country as he made his mark for a Messi-less Albicelestes.
Argentina have had a resurgence of form since a disappointing second-round exit at this summer's World Cup, winning four of their six games under interim coach Lionel Scaloni.
The side looked the livelier of the two in Mendoza, with Victor Guzman having the best chance for Mexico in the opening frame but firing a free kick over the bar.
The second half saw a raft of changes with Paulo Dybala wrapping up the victory six minutes after coming on for Icardi.
Giovanni Simeone sprinted down the wing and played the ball into Dybala who found the right corner on 87 minutes for his first international goal.