The Brit, who had a tough opening match against Marcos Baghdatis, served well throughout the match and hasn’t allowed Bogomolov a single break point.
He will now play either David Nalbandian of Argentina or Ivan Dodig of Croatia.
Rafael Nadal also fought his way into the quarterfinals, defeating Canadian Milos Raonic in straight sets 7-5, 6-3.
The Spaniard will now face Santiago Giraldo of Colombia for a place in the semifinal. Giraldo eliminated Dmitry Tursunov of Russia 6-4, 7-6 (4).
The third quarterfinal match will be decided between the former 2007 champion David Ferrer and Radek Stepanek of Czech Republic.