They won the Sony Ericssson Open title in Miami, and were runners-up in Indian Wells and Montreal.
The three most recent efforts pushed the Belarusian Mirnyi and Israeli Ram up three spots to No. 5 in the 2009 ATP doubles rankings, boosting their chances of qualifying for the prestigious Barclay's ATP World Tour finals in London.
Ram is looking to reach his third straight final in Cincinnati, where he won his first of two ATP World Tour Masters 1000 titles alongside countryman Jonathan Erlich in 2007. They came up just short of the title defence last year when they fell to Bob Bryan and Mike Bryan in the final. Mirnyi is a two-time Cincinnati champion, teaming up with Sweden's Jonas Bjorkman to win back-to-back titles in 2005-06.
Mirnyi and Ram will next confront the top-seeded Bryans, whom they have defeated in two of their three previous meetings this season, including last week in the Montreal semi-finals.
Seventh seeds Wesley Moodie of South Africa and his Belgian partner Dick Norman got a walk-over from Czech Tomas Berdych and Germany Philipp Kohlschreiber as the German complained of fatigue after a tough three-set singles win over German Philipp Petzschner.