Sevastova is currently ranked 19th in the WTA rankings, while Puig is in 70th place.
Sevastova has earned 105 WTA ranking points for reaching the third round of the tournament where she will play Julija Goerges (Germany), who is ranked WTA 10 at the moment.
Puig, who won a close first set, had a double match point halfway through the tie-break in the second set, but Sevastova saved both and moved on to win the set. In the third set, Puig could not put up a fight and Sevastova took the set 6-1.
Sevastova was originally scheduled to play the seventh-seeded Garbine Muguruza (Spain) on Wednesday, but Muguruza withdrew from the tournament due to an injury.