The former champion raced to a 4-1 lead in the first set but the Swiss player was able to fight back and level it, before the Australian broke again to allow himself to serve for a one-set lead.
Wawrinka made a bright start to the second, playing a series of powerful shots from the back of the court to secure a break early on.
However, Hewitt dug deep to get the break back, before a string of errors from Wawrinka gifted the former world number one another break to win the second set.
Wawrinka looked strong in the third set, firing six aces past his opponent, while Hewitt struggled to get his first serve in, giving Wawrinka six break points, but he was unable to convert any of them.
The mistakes crept back into the world number 10's game, giving Hewitt another break, which was enough for him to wrap up the third set and the match.
The 2002 champion will face Germany's Dustin Brown in the next round.