With his brace Messi, the top scorer in MLS, took his tally to nine goals from seven appearances this season.
New England, who had been hit by a virus in the build-up to the game and bottom of the Eastern Conference, delighted the bumper home crowd after just 40 seconds through an Argentine of their own -Tomas Chancalay.
Messi got Miami back on level terms in the 32nd minute when he was found by Robert Taylor's through pass and the 36-year-old made no mistake, slotting home. The eight-times Ballon d'Or winner struck again to put Miami ahead in the 68th minute.
Miami added two more in the final stages - both created by Messi. Substitute Benjamin Cremaschi made it 3-1 in the 83rd minute, pouncing after a Messi shot was parried out. Luis Suarez completed the scoring, finding the top corner after a pass inside from Messi.