Queen’s Club champion Cilic surrendered a two-set lead in stunning fashion, to fall to defeat when he would have been expected to challenge for the title.
Pella battled through 3-6 1-6 6-4 7-6 (7/3) 7-5, toppling last year’s beaten finalist and number three seed.
Cilic was cruising in his two-set lead when showers interrupted play on Wednesday evening, and crucially lost serve in one of the few games to be completed amid the delays.
World number 82 Pella returned with renewed confidence on Thursday, and capitalised fully as Cilic’s game fell apart to reach Wimbledon’s third round for the first time.
Asked how he had conjured victory, Pella told the BBC immediately after coming off court: “I really don’t know because yesterday he was playing so, so good, hitting the ball so hard that I couldn’t do anything.
“The rain helped me a lot, today I played different, tried to be a lot more aggressive.
“I tried to play with more power, and I think in the end that’s why I won.
“Every time you play this kind of player they try to break your serve in the first game because they gain confidence.
“This isn’t my favourite surface but I’m trying to improve.
“After the rain came, and today, I felt much, much better in my game.
“I lost four match points then managed to convert, so I’m very, very happy.”