Pospisil trailed the 53rd-ranked Australian 6-4 in the tiebreaker before reeling off four straight points to take the opening set. An early break in the second proved enough for the seventh-seeded Canadian.
"It's very special for me to beat a former No. 1," said the 23-year-old Pospisil, who won just two games in his only previous match against Hewitt last year in Newport, R.I. "I've come a long way since. I started working with another coach and I've put in a lot of hard work."
Also, Michael Russell of the United States failed to convert any of his 13 break points in a 6-3, 6-4 loss to qualifier Mirza Basic of Bosnia-Herzegovina. Ruben Bemelmans of Belgium had 10 aces while beating Jan Hajek of Czech Republic 6-2, 6-0. Slovakia's Lukas Lacko defeated Austria's Gerald Melzer, brother of former two-time champion Jurgen, 7-6 (5), 6-1.
Miloslav Mecir Jr. of Slovakia stunned Pablo Andujar of Spain 6-4, 6-4 in his first main draw match. The son of 1988 Olympic champion Miloslav Mecir is ranked 240th and came through three qualifying rounds. He had nine aces and never faced a break point.
Earlier, Daniel Brands of Germany beat Andreas Haider-Maurer 6-4, 7-6 (5) despite the Austrian serving 16 aces. The 57th-ranked Brands managed one break in the opening set against the 2010 finalist and held serve throughout to set up a second-round match against top-seeded former champion Jo-Wilfried Tsonga.
Dominic Thiem, playing in only his second ATP event this year, defeated Daniel Gimeno-Traver of Spain 6-4, 5-7, 6-4. The 20-year-old Austrian reached the second round for a third straight year and will play either sixth-seeded Gael Monfils or Marinko Matosevic of Australia.