The world number six wasted no time in taking control of the contest as she went 4-0 up within the opening ten minutes of the match.
She eventually claimed the opening set 6-1 against her opponent from Belarus.
Govortsova looked to be making a game of it when she broke Kerber at the first time of asking in the second set, before going on to hold her next service game.
However, Kerber responded by winning the next six games in succession to book her place in the next round with just 56 minutes played.
She will now face Sara Errani for a place in the quarter-final.