There was no sign of the ankle problems Williams suffered in the first round as she secured an early break to take the first set 6-2 in 39 minutes.
Williams was in the wars once again before the first set finished, smashing herself with a racket on a forehand pass.
After a short break Mugurza tried to rally at the start of the second set, with the opening game going into a 16th minute before Williams finally claimed the crucial break.
The 19-year-old's resistance ended at that stage as Williams strolled to a clean sweep in the second, securing a straight-sets win.
Williams clinched match point with her 10th ace to book a third-round clash with Ayumi Morita.