Federer, Murray cruise through Miami sweatshop
Andy Murray of Great Britain returns a shot to Feliciano Lopez of Spain during the Sony Open at the Crandon Park Tennis Center on March 23, 2014 in Key Biscayne, Florida - by Matthew Stockman
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.
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.
Federer secured his 21st match win of the season when a backhand from the Dutchman floated long.
"I'm feeling really good with my game," said Federer, who next faces French ninth seed Richard Gasquet.
"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.
"I don't know how hot it was, but when we came over at like 9:30 it was already 80 Fahrenheit (23 Celsius) and it was extremely humid. They are not easy conditions," said Murray.
He now faces French 11th seed Jo-Wilfried Tsonga, who outlasted Marcos Baghdatis 4-6, 7-6 (8/6), 7-5.
Murray has won eight of their nine ATP meetings, the most recent last year on grass at Queen's.
- Tsonga fired 16 aces -
Tsonga trailed a set and was down 5-1 in the second-set tiebreaker when he suddenly found some much-needed form, rallying to win after two and a half hours.
The Frenchman fired 16 aces and needed only one break of serve to make the winning difference.
"It seemed like a very tough match," Murray said of Tsonga's win. "A lot of tight games towards the end. He did well to come back."
Also advancing was Chinese world number two Li Na, the reigning Australian Open champion who dispatched American Madison Keys 7-6 (7/3), 6-3.
Li spent nearly an hour surviving the first set, saving two set points on the serve of 38th-ranked Keys.
The American committed a backhand error on her first chance and double-faulted on the second before Li got the break for 5-4 in a set which eventually went into a tiebreaker.
Li won the decider on the first of four set points to seize the momentum. She then saved a pair of break points in the final game and won after one hour, 41 minutes.
"It was a pretty tough match," Li said. "She played well, big serve, big forehand, especially when she was 3-1 down and then come back 5-3 up and served for the first set.
"During that time I didn't think about too much. I say, 'OK, try to hit the ball, try to do what you have to do, and I think saving the set points at least kept me in the first set.
"This changed the match a little bit, because after that I was feeling her level drop."
Li won despite seven double faults, 26 unforced errors and just 11 winners.
She will next tackle either Carla Suarez Navarro or Kaia Kanepi.
Polish third seed Agnieszka Radwanska, last week's Indian Wells runner-up, beat Russia's Elena Vesnina 7-5, 6-3 and next meets highly-rated 19-year-old Ukrainian Elina Svitolina.