Meanwhile, Roger Federer continued his mastery over Stan Wawrinka, but not before getting a fright en route to a 6-7 (7-2), 7-6 (8-6), 6-2 quarter-final victory.
Djokovic had to work for more than two and a half hours to overcome Cilic, the 2016 champion in the combined WTA and ATP event. The 10th-seeded Serb squared the match as the day's second bout of major rain moved in.
After losing his serve, Djokovic bashed his racket on the court three times, sending pieces of the frame flying.
New Zealand minister rides bike to hospital to give birth
She posted pictures of her and her partner enjoying the "beautiful Sunday morning" ride to the hospital to have her labor induced. Ms Genter and her partner previously had two "very sad" miscarriages that she has spoken about in New Zealand media interviews.
Despite pulling double duty, Cilic got the better of Carreno Busta in what was a lengthy first-set tiebreaker, finally clinching it on his fourth set point.
"This seems to be a bit unreal, to be honest, to be back at this level", he said.
The German was in trouble on his next service game, falling behind 15-40. Djokovic broke that streak to go up 4-3 in the opening set, prompting Federer to mutter angrily.
Djokovic only secured his defeat of the Croatian late in the final set, breaking for 5-3 and finishing off the hard-fought victory in the next game.
Reflecting on the loss, Wawrinka said that he is happy to play a high-level tennis and further asserted that he needs to keep improving his game. "That's going to be a new experience for me". Moments later, she covered her face for a joyous cry, wiping the tears away with her sweat-soaked blue wristband.
Three of those wins came over Djokovic, who is 0-5 in the finals.
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West Ham saw familiar defensive frailties return to haunt them as they lost the lead in a 2-1 home defeat to Bournemouth . Theo Walcott set up Richarlison for his headed goal and also scored himself for Everton at Goodison Park.
"I feel like she missed more than me today", Halep said of Barty. "That's very different, playing two matches in one day".
Federer, the second seed, began his tournament with a comfortable 6-4 6-4 win over Peter Gojowczyk after a first-round bye. "I'm really exhausted but I'm happy that I could win both". "I didn't take my chance".
"I could see that he was unhappy, but I thought he was going to play on".
Halep will be ranked No. 1 through the U.S. Open. Halep would become the first woman since 1973 to win Canada and Cincinnati back to back. "I will not complain, but it was a tough day". "But I also take the positive from these two weeks".
Petra Kvitova, a Cincinnati semi-finalist in 2012, reached the last eight with a 6-4, 6-2 win over France's Kristina Mladenovic. Now, it's on to his first Cincinnati final in three years.
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Elizabeth Humphries said: "Appalling Gatwick Airport , with broken monitors and a tiny whiteboard for announcing gates". Pictures emerged on social media of crowds surrounding the board as they tried to get hold of their flight information.