World number two Nadal began the contest brightly and went on to win the opening three games.
Argentine Schwank momentarily stopped the rot by holding his service game, before Nadal saw out the set with another three-game winning streak.
Schwank, who is currently ranked 192 in the world, fared slightly better in the next set. However, he was powerless to prevent the defending champion from wrapping up a 6-3 success.
One break of serve was all that was required in the third set for Nadal to book his place in the final 16.