Neville was appointed in January to lead the team co-owned by former Manchester United team-mate David Beckham - but it was another Old Trafford old boy who had the decisive say as Javier Hernandez scored twice for the Galaxy.
It was also the first game at Miami's DRV PNK Stadium, with seven-time Super Bowl-winning quarterback Tom Brady among the spectators, and Robbie Robinson scored the first goal of the Neville era in first-half stoppage time after Gonzalo Higuain unselfishly squared the ball to him.
Hernandez equalised just after the hour mark with a neat touch and finish from substitute Ethan Zubak's pass but Higuain's penalty restored Miami's lead after Jorge Villafana fouled Rodolfo Pizarro.
Hernandez equalised once more though, from point-blank range after Zubak's glancing header was tipped away, and Sacha Kljestan clipped in an 81st-minute winner.
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