Five-time champion Williams enjoyed a comfortable passage at Arthur Ashe Stadium as she goes in search of three title triumphs in a row at the final grand slam of 2014.
Kanepi reached the last eight at Flushing Meadows in 2010, but the Estonian world number 50 was unable to repeat that performance as she succumbed to the greater power of the American.
Williams made a strong start and Kanepi was forced to save four break points in her opening service game.
The world number one did find the breakthrough she craved in game eight, however, as a couple of forehand errors from Kanepi proved costly.
After saving one set point in the next, two more mistakes from the Estonian saw Williams clinch the first set in just over half an hour, having served six aces rattled off 11 winners.
Williams made an ideal start to the second set with another break and although Kanepi hit back straight away, the American responded in kind to lead 2-1.
A pair of forehand errors from Kanepi handed Williams a double break in game seven, but the number one seed wasted her first chance of sealing victory as her opponent broke back to keep her hopes alive.
An unlikely comeback failed to materialise, however, as a double fault from Kanepi set up match point and an unforced backhand error saw Williams into the last eight, where she will now face Flavia Pennetta.