Fifth-ranked Federer pounded Dutchman Thiemo de Bakker 6-3, 6-3 in just over an hour while British sixth seed Murray downed practice partner Feliciano Lopez 6-4, 6-1 yesterday.
Ivan Lendl, the coach from whom Murray recently parted, was sitting in the player box to watch his former protege's triumph.
Federer, 32, broke for victory in the final game, with de Bakker saving a pair of match points but also double-faulting at a crucial moment.
"I'm feeling really good with my game," said Federer, who next faces French ninth seed Richard Gasquet.
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"My confidence is high and I'm moving well. I'm excited about how I've been playing."
Federer said he will need to gather information on Gasquet, whom he last played in November at the season-ending event in London.
"We've played many times and I'm not sure how he's playing right now," he said. "I have to find out a little bit."
Murray polished his record to 9-0 over Lopez in only 73 minutes. The Scotsman, who does much of his off-season training in Miami, improved to 21-6 in the US city.
He now faces French 11th seed Jo-Wilfried Tsonga, who outlasted Marcos Baghdatis 4-6, 7-6 (8/6), 7-5.