The 14th-seeded Cilic recorded his first victory in three meetings, all at grand slams, over Del Potro with a 5-7, 6-4, 7-5, 5-7, 6-3 victory in four hours, 38 minutes and will now meet Andy Roddick in the quarter-finals.
"Marin is playing great tennis and I think he did better than me," said Del Potro. "The serve in the end (was my downfall). After four hours you have to really focus and he broke me (early) in the fifth. I had my chance but he played very good."
Del Potro, who entered the tournament with a wrist problem, seemed to be troubled with fatigue and other injuries throughout the match and received substantial treatment on his left foot.
"I will go home and see my doctors there and have some rest and recovery before the next tournament," said Del Potro.
Cilic now faces Roddick, who kept his cool to wear down a frustrated Fernando Gonzalez 6-3, 3-6, 4-6, 7-5, 6-2 in a fiery late-night battle. The pair slugged it out for almost three-and-a-half hours at the Rod Laver Arena before Gonzalez gifted Roddick victory with a double fault just after 1am.
"I was lucky to get out of that. I took Fernando's best stuff for the majority of four sets," said Roddick. "Sometimes if you stick around, you get your reward and that's what happened. I got a little lucky tonight (but) sometimes it's better to be lucky than good."
Roddick had been under pressure for most of the match and his emotions were running high as he began arguing with chair umpire Enric Molina.
It was not the first time this week that the American had clashed with the officials and in one of his earlier matches he refused to shake the umpire's hand after an argument over the rules in dealing with Hawkeye challenges.
Roddick admitted he got a lucky break to win the fourth set when he hit a cross-court forehand that was called out by a linesman. He challenged the call and won, forcing the match into a fifth set.
Roddick went straight to his seat but Gonzalez stood his ground and argued the point should have been replayed, saying he had been in a position to hit the ball but withdrew from the shot because the ball was called out. Gonzalez went on to lose his next service game.
"I know he was pretty upset about the challenge and that rule no one seems to know about," Roddick said.
"I still don't know what the rule is. I can certainly sympathise with his frustrations."