Sevastova (WTA No. 12) beat Barthel (WTA No. 76) in two sets with 6-3, 6-1 in a game that lasted just over an hour.
She will next face Romania's Bianca Andreescu (WTA No. 106).
Last year, Sevastova made it to the second round.
Meanwhile Anastastija Ostapenko lost in the first round. She has recently returned to the court after an injury. Latvia's best male tennis player, Ernests Gulbis (ATP No. 86) left the tournament in the first round due to injury.