The 25-year-old Goffin saved four set points in the 12th game of the first set before taking the set in a tiebreaker.
Goffin then breezed through the second set, finishing with seven aces overall in the 97-minute match yesterday at Indian Wells, one of the biggest events on the ATP and WTA calendar outside of the four Grand Slams.
"That first set was a great battle," said Goffin, who broke Cilic three times in the quarter-final. "It was tough to stay focused. "I had a break 5-4 but it is always tough to finish a set."
"I deserve to relax a little bit then be ready for the next round," Goffin said. "First I am going to enjoy this win with my team. "I am really pleased with the way I am playing at the moment. I hope I can keep going."
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Goffin also defeated Cilic on a clay court in Belgium during the Davis Cup first round on March 6.
Goffin's win over Cilic on Thursday comes less than 24 hours after he snapped a 14-match losing streak against top-10 players with a fourth-round shocker over French Open champion Stan Wawrinka.
"For the future, it gives me a lot of confidence. I still don't know where I will be in the future and in the rankings, but I will try to keep improving my game to beat a lot of players like this."
Daria Kasatkina's surprising run at Indian Wells came to an abrupt halt when she was humbled 6-3, 6-2 by 18th-seeded Czech Karolina Pliskova in the women's quarter-finals.
"It was one of the best matches what I played here so far," said Pliskova.
Pliskova, ranked 19th in the world, said the more she plays the better she gets. She is looking to not only go further at Indian Wells but boost her world ranking this week.
"It's important during the next tournaments that I have few matches behind me," she said. "I think I played some good tennis this week. I have chances to go and improve the ranking and get close to the top 10 again."