Substitute Stanciu, who replaced Florin Tanase in the second half, gave keeper Emilis Zubas no chance with a venemous 30-metre drive in the 65th minute.
Romania, who have now gone 16 games without defeat since June 2014, were generally unimpressive in their first match of the year.
Anghel Iordanescu's team, who are 16th in the world, enjoyed most of the possession but lacked ideas against a side ranked 128th.
Centre back Cosmin Moti headed just wide from a corner by Stanciu while Zubas saved a close-range effort by substitute Andrei Ivan early in the second half.
Lithuania, who failed to qualify for Euro 2016, went close to scoring two minutes before the break when keeper Costel Pantilimon parried a 20-metre free kick by Lukas Splavis.
A minute's silence was observed before kickoff after at least 31 people were killed in Tuesday's Brussels attacks.
Romania, who host champions Spain in another friendly on Sunday, have been drawn in Group A with hosts France, Switzerland and Albania at Euro 2016 in June.
(Reporting by Angel Krasimirov; Editing by Tony Jimenez)
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