Camila Giorgi admitted she was still battling to discover her finest form after a topsy-turvy performance against the Latvian, who is ranked 21 in the world.
The Italian was determined to make a fast start and she didn't disappoint, stretching her opponent with her booming forehand.
Giorgi secured the first set 6-1 following a couple of service breaks, but she lost her focus in the second set as Sevastova stepped up her game to level at 6-2.
Roared on by a strong Italian support on Court 8, Giorgi showed great character against an opponent ranked more than 20 places above her.