In a match that lasted 2 hours, 34 minutes, Dimitrov fought off two match points in the eighth game of the third set and forced a tiebreaker, which Wawrinka clinched with an ace.
Wawrinka, who has won the Australian, French and U.S. Opens, next faces qualifier Andrey Rublev, who advanced with a 6-7 (4), 6-4, 6-2 victory over 15th-seeded Nikoloz Basilashvili.
Two-time Australian Open champion Victoria Azarenka, who won Cincinnati in 2013, reached the second round after 12th-seeded Belinda Bencic retired with a left foot injury when trailing 6-4, 1-0.
Tournament officials announced Tuesday that fourth-seeded Dominic Thiem had withdrawn due to illness.