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.
She attacked the net well and with great purpose and showed a new-found aggression to win the decider 6-4 in a match lasting one hour and 55 minutes.
Giorgi will face the winner of the match between Aleksandra Krunic or Madison Brengle in round two.
"It was a tough match, but I was pleased with my level," commented Giorgi after the game.
"I love playing at Wimbledon and coming to London - the most beautiful city.
"I am always warmly received by the crowd and it helps me raise my game."
Attention turns to Dudi Sela on Tuesday as he tackles former champion Rafael Nadal in the second match on Centre Court on Tuesday.
Diego Schwartzman is also in action, against Mirza Basic.
