When rain forced the tie to be postponed on Wednesday, Cilic was leading by two sets against an opponent who had never won a match at Wimbledon before this year.
After breaking Buzarnescu for a second time in the set, Pliskova stepped to the line at 5-1 to complete her massive comeback. She missed last year's tournament while pregnant.
The 36-year-old American now can not meet a top 32 player until the semi-finals after the scattering of the seeds this week.
She rallied to level the third-round match before Rodina sealed a maiden place in the last 16 of a major.
Ninth seed John Isner saved two match points and served 64 aces to overcome Belgian Ruben Bemelmans 6-1 6-4 6-7 (6-8) 6-7 (3-7) 7-5 in three hours 46 minutes to reach the third round.
Keys lost nine games on the trot from 5-2 up in the first set to 0-4 down in the second.
The 11-time French Open champion is looking for his third title at the All England Club and first since 2010.
Red Bull boss warns F1 over 'vanilla-type regulations'
Qualifying begins at 2:00p BST Saturday, 30 June, and the race starts at its now traditional time of 2.10p BST. Sauber duo Charles Leclerc and Marcus Ericsson finished ninth and 10th.
There were a few scary moments in the early going, with Williams at one point down 5-3 in the first set and Mladenovic getting the better of her.
In addition, this was Roger's 335th Grand Slam win and the 94th at Wimbledon, moving closer to that magical number that he could potentially reach in 2019.
Monfils is another fourth round debutant after he knocked out last year's semi-finalist Sam Querrey 5-7 6-4 6-4 6-2. But he easily held serve in the next game and broke Zeballos again to close out the match.
"Yesterday he was playing so, so well and I couldn't do anything". I thought I did very well today.
The 29-year-old Russian needed treatment after securing the decisive break in the final set, but she was able to block out the pain to seal her upset.
Unseeded American Taylor Fritz also unexpectedly took a 2-1 lead over world No. 4 and tournament fourth seed Alexander Zverev before their second round match suspended by darkness. "I felt my mind go and move on".
Meanwhile in the doubles, South Africa's Raven Klaasen and his New Zealand partner Michael Venus advanced to the second round when they defeated Australia duo Lleyton Hewitt and Alex Bolt 7-5, 6-2, 3-6, 6-1.