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The world number one was, as expected, too good for the Brit, securing a 6-3 6-3 victory in 80 minutes at the ATP 1000 event.
Djokovic is a two-time defending champion in Miami and already has three titles this year, and he will take some stopping to deny him a fourth.
The 11-time grand-slam champion lost just nine points on his serve in the first set and that meant he was in control.
Djokovic broke for 2-1 in the second when Edmund sent a forehand into the base of the net after a game lasting almost 10 minutes.
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Edmund hung in there but only until the ninth game, Djokovic converting his first match point when his opponent sent a backhand wide.
Awaiting Djokovic in the third round is Joao Sousa, who edged past Vasek Pospisil.