It was sixth-seeded del Potro's first match inside Arthur Ashe Stadium, and produced his second trip to a Grand Slam semifinal.
"It's so beautiful playing in front of this crowd," del Potro said. "I'm so happy it happened this way."
Jettisoned to smaller courts for every match over his two years at Flushing Meadows - despite his ranking - del Potro finally got to play on the big stage.
The Argentine had a rough time handling Cilic's serve in the first set, but worked it out and rolled off 17 of the last 20 games.
He's in his second major semifinal, following this year's French Open, where he blew a lead and lost in five sets to Roger Federer.
Del Potro's next opponent will be the winner between No. 3 Rafael Nadal and No. 11 Fernando Gonzalez, set for later today.
Del Potro got a matchup with 16th-seeded Cilic thanks to the Croatian's three-set upset of No. 2 Andy Murray on Tuesday. In del Potro, Cilic saw a near mirror image of himself - 6-foot-6 (1.98 meters), big serve, and they were even born five days apart in September 1988.
But Cilic's sharpness from the Murray match vanished in this one after leading by a set and a break. He committed 53 unforced errors against 29 winners, while del Potro was on his game - 24 unforced errors and 27 winners.
Despite wind gusting at more than 20 mph (30 kph), del Potro showed power, and the poise to hit drop shots and lobs.
"I was thinking, every point, do the same, try to put the ball in the court," he said. "When you fight that way to the final point, you have many chances and that's what happened today."
Despite what was at stake, he gave Cilic a point toward the end of the third set when a second serve by Cilic was called out, but del Potro conceded it.
He's the third Argentine to reach the US Open semifinals, after Guillermo Vilas and David Nalbandian.
American duo Todd Parrott and Carly Gullickson won the first trophy to be handed out this week at Flushing Meadows, upsetting defending champions Cara Black of Zimbabwe and Leander Paes of India 6-2, 6-4.
