"I'm pleased with the win," Dimitrov said, via Sky Sports. "Mischa did not make it easy for me with his game. I had to fight to win."
Dimitrov will face world No. 76 Denis Istomin of Uzbekistan on Thursday.
Defending tournament champion Martin Klizan of Slovakia held off Germany's Philipp Kohlschriber 6-7 (5-7), 6-4, 6-1 in second-round play.
Sixth seed Jo-Wilfried Tsonga of France bested Luxemborg's Gilles Miller 6-4, 6-2 and Frenchman Pierre-Hugues Herbert beat Russia's Evgeny Donskoy 6-2, 7-6 (7-4) in their second-round matches.
Third seed David Goffin of Belgium breezed past Russian Andy Kuznetsov 6-3, 6-2 in his Round of 32 match. Kuznetsov won the Sofia Open last week in Bulgaria.
France's Richard Gasquet had no problem brushing aside Serbia's Viktor Troicki 6-4, 6-2 in their round one bout.