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.
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.
Serena, seeded 25 this year after taking time away from the tour to give birth to her daughter, faces Kristina Mladenovic of France for a place in the last 16 later Friday.
The Rise And Fall Of Nawaz Sharif, Pakistan's Three-Time Leader: Timeline
The decision against the Sharifs comes ahead of the July 25 polls, as well as media complaints that the press is being muzzled. He said that Nawaz Sharif attacked institutions just to safeguard his corruption and ill-gotten wealth.
Later Thursday, fifth-seeded Juan Martin del Potro, who made the semi-finals in 2013, tackles 36-year-old Feliciano Lopez, a three-time quarter-finalist, who is playing in a record 66th consecutive major.
Nadal won only 64 per cent of points on his first serve and faced 13 break points - including three in the first game of the match - but he saved 11 of them and converted five of his own to wrap up the win in under 2 1/2 hours on Centre Court. Isner had 113 aces in that match and Mahut hit 103.
Defending champion Roger Federer continued his serene progress at a Wimbledon full of shocks with a straightforward victory over Jan-Lennard Struff. "But I knew if I took my chances today, I could do well".
Cilic last bowed out in the second round in 2013.
We'd be at war with North Korea if it wasn't for me
Physically, we would be able to dismantle the overwhelming bulk of their programs within a year", Bolton said. Collins stressed the need for "verifiable, unimpeded, reliable inspections" of the North's weapons programs.
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. She sat out Wimbledon previous year while pregnant.
Makarova, who has reached the round of 16 at the All England Club for the third time, will next face Italy's Camila Giorgi, who advanced after saving a match point while beating Katerina Siniakova of the Czech Republic 3-6, 7-6 (6), 6-2.
Venus Williams has become the latest former champion to be knocked out at Wimbledon.
His early exit opens up Federer's path to the final even more, with No 8 Kevin Anderson the highest-seeded player left in the Swiss star's half of the draw after No 6 Grigor Dimitrov lost in the first round.
Vettel hits the front, Verstappen hits the wall
On lap 53, he pitted again for super-softs, dropping a place to fifth behind Ricciardo, who nearly immediately slowed and stopped. It meant the likes of Kimi Raikkonen and Max Verstappen emerged ahead of the Brit when he eventually had to pit a few laps later.