The Serbian looked to be cruising in the first set when he went 4-1 ahead, only to then lose his serve twice in a row as Monaco won four games on the spin.
However the top seed - who has finished runner-up in Cincinnati four times in the past five years - then immediately won the next three games. The second set was certainly a procession, Djokovic breaking twice to progress.
"Between 4-1 and 4-5 (first set), four quite bad games for me," he said afterwards. "I stopped moving my legs. I didn't really go for my shots.
"I let him kind of dictate the play and wait for his mistake, which was not the right tactics.
"But all in all, I expected a little bit of a challenge for myself especially because he's a good player but also because it's the first match here in Cincinnati, which has different conditions from what we played in Montreal."
Djokovic is chasing his fourth title of the year but his first since April; he was beaten in the semi-finals in Montreal last week by eventual champion Rafael Nadal.
Juan Martin del Potro, the seventh seed, knocked out Russian Nikolai Davydenko 7-5 7-5 while Canadian Milos Raonic, who has now moved into the top 10 in the rankings for the first time in his career, continued his good form by beating Serbia's Janko Tipsarevic 6-4 7-6 (7/4).