The hosts began the night in a three-way tie at the top with a vastly superior goal difference, and with second and third-place Slovakia and Greece playing each other in Bratislava tonight they took a firmer grasp on a top-two place with ease.
All three goals came in the first half, with Manchester City striker and Bosnia captain Edin Dzeko having a hand in two.
Vedad Ibisevic got the opener just before the half-hour mark, latching on to a pass from Miralem Pjanic and lashing the ball into the top right-hand corner of the net.
Pjanic was again the provider a little over five minutes later, playing in Dzeko to find the bottom corner of the net from short range.
Dzeko then returned the favour to put the game beyond doubt five minutes before the break, passing from the left for Pjanic to fire in.
Lithuania actually had the better of the second half, but the closest they came to scoring was a 63rd minute long-range effort from Mindaugas Panka which Asmir Begovic fumbled before a raised assistant's flag prevented the visitors from following up.