The 84th ranked Swede defeated the 109th ranked Harmony Tan from France in two straight sets: 6-2, 6-4.
Thus, 26-year-old Peterson is on to the round of 16 in the tournament.
There she meets Jaqueline Cristian, ranked 100. The match will be decided on Tuesday afternoon.
It will be a chance for revenge for Peterson who missed the final of the WTA tournament in Romania just over a week ago when she fell in the semifinals against Anett Kontaveit (3-6, 2-6).
Also in the tournament in Linz are also this year's US open winners Emma Raducanu and Simona Halep.