Kanepi fought valiantly in the first game as she saved three break points, but Kerber was not to be denied and took it at the fourth time of asking.
From that point on it was a one-sided first set as Kerber dropped just five points in the next four games, breaking Kanepi twice along the way to take a 5-0 lead.
The final game of the set proved a little more problematic, but Kerber eventually wrapped up the 6-0 win with her third set point.
Kanepi put up more of a fight in the second set as she fought back from two break points to take the first game, but Kerber again showed her dominance by winning the next three to take a 3-1 lead.
The number eight seed broke once more to make it 5-2 but Kanepi showed a little resolve by breaking back immediately to prevent Kerber from serving out the set.
The Estonian was merely delaying the inevitable, however, as Kerber sealed the match in her next service game to book her place in the fourth round.