The 31-year-old Czech blasted 16 aces to overpower his Kazakh opponent in two sets and secure his quarterfinal berth.
Fourth-seed Bernard Tomic of Australia won a two-hour duel with American qualifier Ryan Harrison, 6-4, 4-6, 7-5.
The 23-year-old right hander hit only 10 aces to Harrison's 20, but held off the American's challenge, saving three break points to book a clash with Brazilian Thomaz Bellucci in the quarterfinals.
It was their second head-to-head clash in an ATP competition, with Tomic winning their last meeting in 2012.
For his part the 28-year-old Bellucci notched a two-set victory over Italy's Thomas Fabbiano, knocking down 13 aces to the Italian's five, to advance to the quarterfinals.
