Djokovic will next face either fifth seed Dimitrov or Zverev.
Stephens the defending U.S. Open champion overcame a thumb injury during a 6-3, 6-2 victory over qualifier Tatjana Maria.
"I think it adds more to the motivation rather than pressure", the 30-time Masters champion said.
Djokovic - a five-time finalist at the ATP Masters 1000 event as he seeks to become the first man to complete the Career Golden Masters - was sloppy early but recovered by break five times en route to victory.
He also has won all four Grand Slam titles (six Australian Opens, one French Open, four Wimbledons and two US Opens) and is a five-time victor of the elite season-ending ATP Finals. "I really want to win this tournament". I'm still in the tournament this year, and hopefully I can get a shot at the title.
After a lengthy rain delay mid-afternoon, a final deluge just before 11pm finished off play as Juan Martin del Potro and Hyeon Chung never got started after warmup.
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It does not get any easier for Djokovic, with Dimitrov waiting in the next round.
'It's normal to expect that you have new faces on the tour, Zverev, who is now established top 3, 4, 5 player in the world for quite a long time", said Novak. "You know, Tsitsipas, Coric, Shapovalov, you have a lot of those NextGen players that are making their mark in the tennis, and this is the new generation this is coming in. Robin Haase beat third-seeded Alexander Zverev 5-7, 6-4, 7-5 for his first victory against a Top 10 opponent since he beat Zverev last November.
Haase will meet Spain's Pablo Carreno Busta in the third round after the 13th seed beat Bradley Klahn 6-4 6-4.
Cilic - who will take on Karen Khachanov - was playing his first Cincinnati match since winning the title in 2016.
Aryna Sabalenka of Belarus continued her successful tournament debut, beating ninth seed Karolina Pliskova 2-6, 6-3, 7-5.
Three-time Grand Slam victor Stan Wawrinka continued his return after knee surgery a year ago by beating Kei Nishikori 6-4 6-4, and Nick Kyrgios saw off Croatian Borna Coric 7-6 (7-1) 0-6 6-3.