It was the second loss in six days for the Swiss champion, who was beaten by Juan Martin del Potro in the Indian Wells final and is set to lose his top ranking to Rafa Nadal even though the Spaniard is not playing in Miami.
Kokkinakis, ranked 175th in the world, used a vicious top-spin forehand to wear down the defending champion and claim an upset victory in front of a stunned near-capacity crowd.
Kokkinakis, 21, only got into the Miami qualifiers on a wildcard but he displayed the talent that has long had him earmarked as one to watch, improving the longer the match progressed.
Federer looked to be taking care of business as usual when he broke Kokkinakis in the fourth game of the opening set.
There were few danger signs for 20-times grand slam champion Federer until he was broken to love in the fourth game of the second set as his first serve deserted him.
Sensing vulnerability, Kokkinakis pounced and the whole tone of the match shifted.
He won the set on serve to cursory applause and the decider was finely balanced throughout.
Kokkinakis displayed poise beyond his years to go toe-to-toe with the 36-year-old Federer and dominated the tiebreak, winning on a second serve that Federer sent into the net.
Kokkinakis let out a primal scream as the small Australian contingent in the crowd celebrated, leaving Federer to walk off the Crandon Park court for the final time, before the event moves to a new venue next year.
