Stuttgart striker Vedad Ibisevic was the man of the night, scoring a 68th-minute goal in this decisive Group G qualifier.
Since gaining independence from the former Yugoslavia in 1992, the Bosnians have agonisingly all too often tripped up at the last qualifying hurdle, as they did against Portugal in the play-offs for South Africa 2010 and UEFA EURO 2012.
With Greece taking a seventh-minute lead against Liechtenstein in Athens to assume the Group G summit, the task facing the Safet Susic-coached side was at least clear cut, a win now being essential to grab the automatic qualifying spot on goal difference from the goal-shy Greeks.
After Lithuania's Mindaugas Kalonas tried a daring half-volley on 25 minutes the Bosnians began to cause problems and will have counted themselves unlucky not to have reached the break in front.
Lithuania keeper Giederius Arlauskas had to look lively two minutes from the interval to deny Sejad Salihovic's deflected shot, leaping across his goalmouth to maintain the stalemate.
Desperate to avoid the play-offs Bosnia emerged for the second half intent on finding a way past the in-form Arlauskas.
The Lithuanian player made his third save from a Miralem Pjanic free-kick minutes after the restart, with Ermin Bicakcic volleying the rebound high.
Then, with the clock ticking, Ibisevic finally put Bosnia in World Cup heaven. Set up by Edin Dzeko from the left, the 29-year-old side-footed past Arlauskas to secure Bosnia top spot in Group G and their long-awaited and fully deserved ticket to Brazil next year.