Dimitrov beat Zizou Bergs 6-3, 3-6, 6-2 to reach the third round, where he faced Canadian Open champion Alexei Popyrin.
Both players defended their serves extremely well in the opening set, and thus forced a tie-break.
Dimitrov edged out Popyrin in it to take a one-set lead.
He raced to the finish line in the second set as he swept five games in a row to secure a 7-6 (5), 6-2 win, and advanced to the fourth round here for the third consecutive edition.
Mensik, meanwhile, ousted Pedro Martinez in his opener here, and then overcame a one-set deficit to stun sixth seed Andrey Rublev 6-7 (7), 6-4, 6-3 in the second round.
He was up against Alexander Shevchenko in the third round.
The Czech teen cruised through the first set, and claimed it for the loss of only one game.
He blew a 3-1 head start in the second set, which came back to bite him as Shevchenko captured the set in the eventual tie-break.
Dimitrov was on a roll against Popyrin in the previous round.
He won a massive 97 percent of his first-serve points, and didn’t face a single break point during the match.
He struck 18 winners in contrast to 17 unforced errors. It also marked his 40th win of the season.
Dimitrov also has a 14-2 record on hardcourts against players ranked outside the top 50, and 10 of those wins have been in straight sets.
Given his record against lower-ranked opposition, he will be favored to one-up Mensik this time.