The Lokomotiv Moscow stopper became the first player born outside of Russia to represent the national team when he replaced Stanislav Kritsyuk.
The 30-year-old Guilherme, who received his Russian passport last year, had little to do as the European Championship finalists eased to a comfortable win.
Fedor Smolov scored five minutes before halftime while Alexander Golovin and Denis Glushakov were on target after the break for Leonid Slutskiy's side.
Coach Slutskiy named a largely experiential lineup with only Sergei Ignashevich and Igor Smolnikov likely to start their first Euro 2016 game against England in Marseille on June 11.
Smolov was given a chance to stake his claim for a place at the finals in France and the Krasnodar forward impressed in a 45-minute outing.
He broke the deadlock in the 40th minute with an excellent left-foot finish beyond keeper Vytautas Cerniauskas after being sent clear by Dmitri Tarasov's pass.
It was Smolov's fifth goal on his 11th international appearance.
Substitute Golovin then made it 2-0 after pouncing on a knock-down from Alexander Kerzhakov.
Glushakov made sure of the win when he headed the ball in at the near post following a corner.
Lithuania failed to qualify for Euro 2016.
(Editing by Tony Jimenez)
