Pospisil trailed the now 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 in Newport last year. "I've come a long way since. I started working with another coach and I've put in a lot of hard work."
The native of Vernon, B.C., next plays Robin Haase. The Dutchman, who won both of his career titles in Austria, rallied to beat Ilija Bozoljac of Serbia 5-7, 6-2, 6-2.
After winning the demanding opening set in 52 minutes, Pospisil broke Hewitt's serve to start the second set and held the margin out to his 14th victory of his breakthrough season.
He finished the match with 12 aces.
"It was a tough match and conditions were a lot different than they've been the last few weeks in Asia," said Pospisil, whose goal for the season is a top 32 finish and seeding at the Australian Open in January.
"I had to make some adjustments but I did. I'm very excited with my performance today. it's great to have such a win over a player like Hewitt. It's still very special to beat him, there are not many players like him. I think my hard work this season is really paying off as we get near the end."
Pospisil said that after winning the opening tiebreaker, he was able to consolidate his success with the early break in the second set.
"I got lucky on the deuce points, hitting a frame lob. But I had momentum, from the tiebreak and I wanted to continue that.
"Hewitt had some chances but after I got the break it was relatively comfortable to serve my way though the match."
Pospisil is joined in the Vienna field by Toronto's Daniel Nestor, playing as the doubles third seed as he teams with Austrian Julian Knowle this week. Knowle is the regular partner of Jurgen Melzer, who had to withdraw from his home event as his season ended early with a shoulder injury.
In other results, the son of 1988 Olympic champion Miloslav Mecir stunned Pablo Andujar of Spain 6-4, 6-4 in his first ever main draw match. The 25-year-old Miloslav Mecir Jr. of Slovakia, who is ranked 240th and came through three qualifying rounds, served 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.
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, and Ruben Bemelmans of Belgium had 10 aces while beating Jan Hajek of Czech Republic 6-2, 6-0.
— With files from The Canadian Press.