Cilic was runner-up to Roger Federer past year and showed great form by beating Novak Djokovic in the Queen's Club final last month.
The only past Wimbledon champion remaining in the field?
And the world number 82 held his nerve to convert his fourth match point and win 3-6 1-6 6-4 7-6 (7-4) 7-5.
Federer, making his 20th consecutive appearance at the grass-court Grand Slam, is yet to face a break point from his opening three matches and will now continue his campaign against 22nd-seed Adrian Mannarino.
John Isner, the USA ninth seed, saved two match points, fired 64 aces and 88 winners to defeat Belgian qualifier Ruben Bemelmans 6-1, 6-4, 6-7 (6/8), 6-7 (3/7), 7-5. The American fought back from a set and two breaks down only to falter near the end.
Keys lost nine games on the trot from 5-2 up in the first set to 0-4 down in the second. But Keys won the next five games and broke again to level the set score. After the double fault in the first set, Mladenovic appeared to lose her confidence. I thought I did very well today.More news: Harry Kane, Dele Alli 'fitness concerns for quarter-final'
"It's a wonderful feeling walking out there, I try to put on a good match and try hard every time, regardless of how many times I've played at Wimbledon. I feel ready to compete".
The big Argentine, in the same half of the draw as Nadal, was dominant throughout against the 36-year-old at his 66th consecutive grand slam tournament.
"Of course, I am surprised a little bit", Rodina said afterward, "because I won".
Barty came back from 2-5 down in the second set to see off 2014 runner-up Bouchard who came through qualifying this year.
"I felt much more confident in my game, I served better and I felt so pumped", said Pella, who reached the third round of a major for the first time.