The Red Bulls had threatened to deliver another upset after Alexander Hack bundled home a 14th-minute opener.
But Messi swiftly orchestrated Inter Miami's recovery from that setback, providing a sublime pass to set up former Barcelona team-mate Jordi Alba's equaliser. Messi then combined with Alba for Miami's second goal, for Telasco Segovia to prod home on 27 minutes.
Segovia then swept in his second of the night deep into first-half stoppage time to leave Miami firmly in control.
A majestic through ball by another former Barcelona team-mate, Sergio Busquets, sent the Argentine World Cup-winner racing through on goal in the 60th minute.
Messi took his time and coolly feinted to wrongfoot Red Bulls goalkeeper Carlos Coronel before tucking away the finish for 4-1. Another Barcelona old boys combination delivered Messi's second.