His 6-4, 3-6, 6-3 win moved him one victory away from the only ATP Masters 1000 title he has never claimed. Djokovic is trying to become the first player to win all nine events since the series started in 1990.
One big hurdle: a potential rematch with Roger Federer, who faced David Goffin in the other semifinal. Federer has won an unprecedented seven Cincinnati titles, beating Djokovic three times in championship matches.
"It's been a roller-coaster week with matches and the interruptions with the rain and all that's happened," Djokovic said.
Djokovic completed his long recovery from elbow surgery by winning Wimbledon for the fourth time last month. He then set out to get his hard-court game in form for the US Open.
Along the way, he wants to get a title in Cincinnati, where he's 0-5 in the final.
Frustrated by his ragged play early in his semifinal win over Milos Raonic, Djokovic slammed his racket on the court, sending pieces of the frame into the air. The racket-busting became a turning point.
When he closed out the victory Saturday, he walked calmly to the net to congratulate Cilic and then raised both arms in triumph.
Bertens is an unexpected finalist, winning only one match in her three previous appearances in Cincinnati. Her only title this season was at Charleston.
Known as more of a clay-court player, Bertens has reached a hard-court final for the first time, spending more time getting accustomed to the different style of play.
"I think also I'm less stressed," Bertens said. "So before the match, I'm less nervous than I used to be. Before I was like, 'Oh, I play on center court, and a lot of people are watching.' But now I'm just more relaxed."
Top-ranked Simona Halep played later Saturday against Aryna Sabalenka, trying to reach the finals for the third time. Halep has never won a Cincinnati title, losing the final match last year to Garbine Muguruza.
A week of rain delays and double-duty days wore on players, many of whom wound up playing twice in a day. Kvitova faded in her second straight three-set match, ending her best showing in Cincinnati. She had made five previous appearances in semifinals this season, winning each tournament.
"My legs were pretty heavy," Kvitova said. "I just couldn't really jump at all. It was very, very tiring, the second set, and I just think that I couldn't really find energy in the third one. I was really trying, but nothing."