Roger Federer's match against Leonardo Mayer was postponed until Friday as well, along with several others pushed back by day-long rain that made a mess of the brackets.
Djokovic came to Cincinnati hoping to build on the momentum of his Wimbledon title and get in shape for a deep run in the U.S. Open. He also dearly wants to win the only ATP Masters 1000 title that has eluded him - nobody has won all nine.
He and Dimitrov split the first two sets and then headed inside for a long rain delay. Djokovic broke Dimitrov to go up 2-1 in the third set, and more rain prompted play to be called off for the night. They'll resume in the morning.
In the women's bracket, Madison Keys used her forehand to beat Angelique Kerber - one of her toughest matchups - and advance to the quarterfinals in-between the storms.
Keys had lost five straight matches against No. 4 Kerber, but turned to her forehand to rally for a 2-6, 7-6 (3), 6-4 victory. She hit 35 forehand winners , including the match-ending shot for her first Cincinnati quarterfinals.
She's expecting a lot of attention at the U.S. Open, where she reached the final last year and lost to Sloane Stephens - her best showing in a Grand Slam event.
"I think it's the first time I'm going to have to be someone defending, getting to the finals of a Slam," she said. "I have never done it. That's going to be a new experience for me."
Stephens didn't fare so well, getting upset by Elise Mertens 7-6 (8), 6-2. The third-ranked Stephens couldn't overcome 37 unforced errors that helped Mertens get only her second career win over a Top 5 player.
Play began with three matches held over from the previous night. Top-ranked Simona Halep faced the most unusual challenge.
Fresh off her second Rogers Cup title, Halep arrived in Cincinnati looking to extend her momentum. On Wednesday night, she appeared to aggravate her lower back on a 105 mph serve during the second set against qualifier Ajla Tomljanovic. After dropping the first three games of the final set, she took a medical timeout for treatment.
Halep returned to the court and took control, running off four straight games for a 4-3 lead when rain arrived. Seventeen hours later, she was back on court and needed only 5 minutes and eight points to complete the 4-6, 6-3, 6-3 win Thursday afternoon.
"I have learned that I don't have to give up, because anything can happen," she said.
Halep was scheduled to then face Ashleigh Barty in the final match of the day, but it, too, was rescheduled for Friday morning.
Two other second-round matches were completed on Thursday as well.
Amanda Anisimova beat qualifier Petra Martic 6-4, 6-3 in a match suspended overnight. Fourth-seeded Juan Martin del Potro beat Hyeon Chung 6-2, 6-3, finally completing the second round in late afternoon. The winners faced the challenge of playing essentially two full matches in one day.
They were spared when the late rain moved in.
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