At 138, the Kazakh is ranked 24 places above Ward in the world rankings, but that counted for little as the Brit closed out a straightforward victory.
Ward was clinical when he earned break point chances, converting four of the six he earned, including one to seal the match.
After winning in 78 minutes, Ward is one more victory away from the main draw.
Elsewhere in qualifying, Dan Evans failed to advance after losing to Bjorn Phau of Germany 7-6(4) 6-0.
The hero in Britain's Davis Cup tie against Slovakia last month lost a tight first set, but won just six points in the second set as he bowed out.