Olympic champion Murray, still seeking his first Grand Slam title after four losses in finals, eked out a 7-6 (5), 7-6 (5), 4-6, 7-6 (4) victory over No. 30 Feliciano Lopez, who led in each of the three tiebreakers before faltering.
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"Could have gone either way," Murray acknowledged. "It was very hot and humid in the middle part of the match. I was struggling a bit with that."
The biggest moment came a few minutes before the fourth-set tiebreaker when Murray saved a break point in a 24-stroke rally in which he drew Lopez into the net, then pushed him back and finally got him to net a backhand to push the game to deuce.
"He came to the net, there was a drop shot, I made a good volley cross court. Points like that can change the match."
The man he beat for the gold at the Olympics, and lost to in the Wimbledon final, Federer, was barely bothered while dismissing No. 25 Fernando Verdasco 6-3, 6-4, 6-4.
Five of Federer's record 17 Grand Slam titles came at Flushing Meadows, and he's looking capable of adding to those numbers.
The Swiss did an unusual amount of damage at the net, closing out 26 of 27 points from the front court. Federer added that effort to the 32 points he won in 47 trips to the net two nights earlier in a second-round win over Bjorn Phau.
"I really tried to play offensive against ... Phau in my second match," Federer said. "I did lose more points than I was hoping to. But I think that gave me the confidence to move forward today. And conditions helped that because it was quicker during the day."
Federer next will take on No. 23 Mardy Fish, who needed to set aside 75 unforced errors over more than 3 hours to beat No. 16 Gilles Simon 6-1, 5-7, 7-6 (5), 6-3 in a match that ended after 1 a.m. Sunday.
Other men's winners Saturday included No. 11 Nicolas Almagro, who ended the run of 19-year-old American Jack Sock 7-6 (3), 6-7 (4), 7-6 (2), 6-1; No. 12 Marin Cilic, who defeated No. 17 Kei Nishikori; and 50th-ranked Martin Klizan of Slovakia, who beat No. 32 Jeremy Chardy.
The previous time these two women played each other, it wasn't close, either. The difference, surprisingly, was that Makarova won 6-2, 6-3 in the fourth round at the Australian Open.
That loss remains the only one for Williams in 22 Grand Slam matches against left-handers.
"Definitely was motivated. Knowing that I lost; could definitely happen again. Did not want that to happen," said Williams.
Williams has dropped only 12 games entering her fourth-round match against 82nd-round Andrea Hlavackova of Czech Republic. Hlavackova, the 2011 French Open doubles champion, bawled on court after her 5-7, 6-4, 6-4 win over 14th-seeded Maria Kirilenko.
"I was feeling like I was melting there," Radwanska said. "I survived the match."
Four-time grand slam tournament winner and former No. 1-ranked player Kim Clijsters headed into retirement after she and Bob Bryan lost their second-round mixed doubles match against Makarova and Bruno Soares. Clijsters announced months ago the U.S. Open would be her last tournament, and she already was out of singles and women's doubles.
Clijsters bid adieu to the sport with her husband and 4-year-old daughter sitting in the stands at Court 17.
"I've been telling her I'm going to be home a lot when this tournament is completely done," Clijsters said. "I don't think she understands the meaning of the word `retirement.'
Former No. 1 Ana Ivanovic overcame a poor start, 56 unforced errors and a partisan crowd to beat 19-year-old American Sloane Stephens 6-7 (4), 6-4, 6-2. Ivanovic also eliminated Stephens in the third round at Flushing Meadows a year ago.