Kick-off was delayed by 95 minutes because of a thunderstorm, but once the match got underway, Messi took little time to settle down and opened the scoring in the seventh minute.
The Argentine began his move at the halfway line and made a run into the box as Robert Taylor (28) chipped the ball over several defenders. Messi then chested down the ball and volleyed home from the edge of the six-yard box.
Orlando equalised 10 minutes later when Uruguayan midfielder Cesar Araujo (22) pounced on a loose ball off a corner and fired it home, but Miami restored their advantage three minutes into the second half when Josef Martinez (30) scored from the penalty spot.
Taylor and Martinez then combined in the 72nd minute on a counter-attack to set up Messi for another close-range volley and the unmarked Argentine made no mistake to beat Pedro Gallese in Orlando's goal.
It was Messi's fifth goal in three games, after he scored against Cruz Azul and Atlanta United in the group stage of the tournament.
Araujo thought he had pulled one back for Orlando in the ninth minute of injury time with a tap-in at the far post but the goal was ruled out by video-assisted review for being offside.
Miami will next face FC Dallas, who beat Mexican side Mazatlan 2-1.
