Sock, who battled back from a two-set deficit to beat the Croat in a Davis Cup duel in July, was impeccable on serve as he did not face a single break point while converting four of six break opportunities against the seventh-seeded Cilic.
"My first time in the fourth round here," 26th seed Sock said in an on-court interview after dismissing the 2014 U.S. Open winner. "It was a big match for me, a big goal of mine."
Sock came to Flushing Meadows riding a high as a double medallist at the Rio Olympics with hopes to maintain the momentum after claiming a bronze in doubles with compatriot Steve Johnson and gold in mixed doubles with Bethanie Mattek-Sands.
With his win at Louis Armstrong Stadium, the 23-year-old Sock matched his previous best grand slam advance, having reached the fourth round at last year's French Open.
His opponent in the last 16 will be ninth-seeded Frenchman Jo-Wilfried Tsonga, a straight sets winner against South African 23rd seed Kevin Anderson.
"There's nothing better than playing in front of the home crowd here in New York," Sock said. "I put it out there on the line on every point."
Sock blasted 10 forehand winners, often in big moments, and served seven aces to six for the big-hitting Cilic, and won 86 percent of the first serves he put in play.
The rising American ended a strong run by the Croat, who captured his first ATP Masters 1000 title last month at Cincinnati and had won 18 of his last 20 U.S. Open matches.
Sock, winner of the 2010 U.S. Open boys' tournament, had been 1-5 in third-round matches at the slams but said he has grown as a player.
"I think with every year, every tournament, every experience can only help," Sock told reporters. "I think I'm putting things together better and better. I definitely feel more confident out there in everything I'm doing."
Sock said improving his return of serve has been a key.
"Returning was big for me. I think I've gotten a pretty good hold on that. Feeling comfortable. Getting in a lot of guys' service games now," he said.
"Overall, I feel my purpose out there. I'm executing it well and I feel like I know what I'm going to do on almost every point."
(Editing by Frank Pingue and Mark Lamport-Stokes)
