Shannon McGregor and Kit Loferski sent Celtic through to the Women's Champions League second round at the expense of section hosts Gintra.
Lucy Ashworth-Clifford's corners caused the Lithuanian side problems early in the match as Elena Sadiku's side controlled the opening stages.
McGregor spotted goalkeeper Liisa Tuomi off her line and sent a long-range effort into the top corner for the opener - her first Celtic goal.
The visitors had the chance to double their advantage before half-time after Saoirse Noonan was fouled while shooting against the post. However, Tuomi smacked away Mathilde Carstens' effort and the rebound was wide.
Kelly Clark was denied by Tuomi and Caitlin Hayes headed wide as Celtic sought a second after the break. It eventually came through Loferski's header from a Jenny Smith cross.
Sadiku's side, who beat Finland's KuPS in Wednesday's semi-final, go into Monday's draw for round two, which precedes the group stage.
The two-legged tie will be played over the final two midweeks in September with the group stage running from October through December.