After scoring 21 times in their first two group games, 2010 world champions Lithuania then lost one and drew two as they struggled to maintain their high level of play.
But, in a repeat of the Beijing 2008 final, Lithuania produced a fantastic second-half performance against China. With the score 2-1 at half time, the European side were then rampant after the interval as Marius Zibolis took his tally in the match to six goals.
Lithuania coach Karolis Levickis said: 'I feel satisfaction about winning, but this is just the first step. There's no way back now. Either you're going to do it, or you're not.'
Lithuania now face Brazil in the semi-finals, who saw off Belgium 3-0 thanks to two penalties from Roman Diego Marques and another goal from Alexsander Almeida Maciel Celente in a repeat of the group game won by the South Americans 12-5.
Turkey, who came from behind to beat Algeria 3-1, will now face Finland - who beat the previously unbeaten Iran 5-1 thanks to a hat-trick from Petri Posio.
Mohamed Mokrane's 16th goal of the tournament saw Algeria lead 1-0 with only seven minutes still to play, but a late hat-trick from Tuncay Karakaya saw Turkey maintain their unbeaten run at London 2012.
In the women's Goalball competition, world champions China remain the team to beat and further demonstrated their attacking strength and technical brilliance with a near flawless performance in beating defending Paralympic gold medallists the USA 5-0 in the quarter-finals.
The tournament favourites now face a Finland side who went into the knock-out stages with just one win to their name from the group stages, but who saw off Canada 2-1 in their last-eight clash.
After a goalless first half, Whitney Bogart put Canada ahead but Katja Heikkinen levelled to take the game into a golden goal overtime period, where the Finland player scored her second to win the match.
Extra-time was also needed to separate Sweden and Great Britain. Anna Sharkey saved a second-half penalty and then put the Host Nation in front before Sweden levelled a minute later through Malin Gustavsson, who then scored the all-important sudden-death goal.
The Swedes now face Japan in the semi-finals, who beat Brazil 2-0 in their quarter-finals thanks to goals from Masae Komiya and Akiko Adachi, who also saved a penalty for her side.