From 2-1 down in the first set, Thiem won the next seven games to take the set and go a break up in the second as Haider-Maurer struggled with his serve.
Errors from Thiem helped Haider-Maurer to level the score at 4-4 in the second set, but Thiem cruised to victory in the tiebreak.
The 22-year-old Thiem, who is chasing his fourth ATP title of a breakthrough season, had not played since losing to Kevin Anderson in the third round of the U.S. Open 18 days earlier.
''My last match was a long time ago, so it's always hard to play your first match, especially against Andy,'' Thiem said in televised comments. ''It's a good start to the tournament and I hope it goes on like this.''
Eighth-seeded Mikhail Kukushkin of Kazakshtan went out in the first round, beaten 7-6 (4), 2-6, 6-2 by Uzbekistan's Denis Istomin.
In Wednesday's other first-round matches, Joao Sousa of Portugal was slow to find his rhythm against Moldovan qualifier Radu Albot, but eventually came through 3-6, 7-5, 6-4.
Sousa next faces Marcel Granollers of Spain, who saw off Thanasi Kokkinakis of Australia 6-3, 6-3.
Italy's Simone Bolelli overcame the aggressive Russian 17-year-old Andrei Rublev 4-6, 6-3, 6-1 to line up a match against top-seeded Tomas Berdych.
The highest-ranked Russian remaining in the draw, Teymuraz Gabashvili, reached the second round with ease, knocking out Belarusian qualifier Yaroslav Shyla 6-2, 6-2.