Britain's Murray needed only 57 minutes to dispatch Australia's Bernard Tomic 6-3, 6-1.
His next opponent will be 29th-seeded Bulgarian Grigor Dimitrov, who advanced when his opponent, Italian Simone Bolelli, retired in the second set with an injury.
The fourth-seeded Berdych needed three sets to get past Spaniard Daniel Gimeono-Traver. The Czech star rallied with a second-set tiebreaker before going on to post a 5-7, 7-6 (7-3), 6-2 victory.
France's Jo-Wilfred Tsonga shook off an extended first set to record a 7-6 (8-6), 6-3 win over Serbia's Viktor Troicki Saturday, and eighth-seeded countryman Richard Gasquet beat Belgian qualifier Olivier Rochus 7-5, 6-2.
Other second-round winners included Spain's 10th-seeded Nicolas Almagro, Finland's Jarkko Nieminen, 16th-seeded Andreas Seppi of Italy, American Sam Querrey, Russia's Mikhail Youzhny and 20th-seeded John Isner of the United States.
Swim Week Miami Beach 2014 [PHOTOS]