Federer was locked in a tight battle with Cilic, after he dropped the second set and then found himself knotted at 4-4 in the third. But the Swiss stalwart broke the tall Croat for a 5-4 edge and then consolidated the break with a set-winning hold. He would cruise the rest of the way in a match that ended when Cilic netted a backhand return after 2 hours, 40 minutes of tennis.
Cilic tallied 44 unforced errors and had his serve broken five times by one of the all-time greats.
"I thought it was a tough match," Federer said. "Coming in I knew it was gonna be tricky, and I'm happy that I was able to counter his pace and his good play."
The 30-year-old Federer titled here five straight years from 2004-08 and was the 2009 runner-up to Juan Martin del Potro. He owns a men's record 16 Grand Slam titles and was this year's French Open runner-up to Rafael Nadal.
Federer has now reached the fourth round in New York 11 straight years.
The eighth-seeded Fish continued his fine summer with a tough 6-4, 7-6 (7-4), 7-6 (7-3) victory over 6-foot-8 South African slugger Kevin Anderson. The American swatted 12 aces and moved on in 3 hours, 20 minutes at Armstrong Stadium.
Fish recently titled in Atlanta and was a runner-up in Los Angeles and at an ATP Masters event in Montreal.
The 29-year-old Fish, who captured the U.S. Open Series heading up to the U.S. Open, could win $2.8 million if he can title here next week.
Former Wimbledon runner-up Tomas Berdych came up a third-round loser on Day 6. Gritty Serb Janko Tipsarevic, seeded 20th, was leading the ninth-seeded Berdych 6-4, 5-0 when the big Czech due to a right shoulder injury.
Berdych, who reached the quarterfinals at this year's Australian Open, was last year's Wimbledon runner-up to the former No. 1 Nadal.
Another former world No. 1, Juan Carlos Ferrero, reached the round of 16 when his opponent retired on Saturday. The unseeded former U.S. Open runner-up Ferrero was leading 31st-seeded fellow Spaniard Marcel Granollers 6-1, 4-3 when Granollers quit.
The former French Open champion Ferrero, the 2003 U.S. Open runner-up to American Andy Roddick, will meet Tipsarevic in his next outing.