Second seed Blake traded service breaks with Kuznetsov in the opening set and grabbed the momentum in the match by winning the tiebreak 7-4.
Ranked ninth in the world, Blake held fellow American Kuznetsov to only 18 points in the second set, closing out victory in 77 minutes.
Blake, who also defeated Kuznetsov this year's Australian Open, reached the U.S. Clay Court quarters for the fifth time in seven appearances.
Battling Blake for a spot in the semi-finals will be Argentine Juan Monaco, who needed only 65 minutes to knock out American Amer Delic 6-2 6-3.
