"It was one of the best matches of my career from start to finish," Cilic told Alex Corretja in his on-court interview.
The 20th-seeded Cilic is into the Roland-Garros last-eight stage for a third time in 16 appearances, and first since 2018.
He will take on No.7 seed Andrey Rublev for a place in the final four.
Iga survives
"QF #3. Love you, Paris," wrote Iga Swiatek on the camera lens following her tightly-contested fourth-round victory over talented teenager Zheng Qinwen on Monday.
The 19-year-old Chinese is the first player to take a set off of Swiatek this tournament and the first since Liudmila Samsonova stretched the world No.1 to three sets in the Stuttgart semi-finals last month.
Zheng took an 82-minute opening set before a right thigh injury began to bother her. Swiatek recovered to post a 6-7(5), 6-0, 6-2 victory, extending her winning streak to 32 consecutive matches.
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The 20-year-old Pole has now matched the third-longest winning streak on the women's tour this century, equalling Justine Henin's run of 32 in a row from 2008.
Swiatek, a champion at Roland-Garros in 2020, next faces 11th seed Jessica Pegula, who also rallied back from a set down in her fourth round against Irina-Camelia Begu.