[Read: France beat Nigeria 2-0]
Germany claimed a hard-fought 2-1 victory over a motivated Algerian side at the Estadio Beira-Rio here, reports Xinhua.
The North Africans had Germany rattled for long spells but Germany eventually ensured their progress to the quarters where they will take on France.
After a tense regular time, both sides were tied at 0-0. But the extra time turned out to be a scoring show.
No more than 90 seconds into the extra time, Schurrle beat the defender to the near post using a clever back heel flick to put the ball into the net.
In the injury time of the extra time, Ozil and Schurrle put together a few nice passes in the box, Schurrle's first shot was blocked by Algerian defender, but the rebound was finished into the top corner by Ozil.
However the Algerian side, playing in their first round of 16 match ever, still didn't give up.
Substitute Abdelmoumene Djabou received the cross brilliantly in the final minute and found the back of the net, but it was too late for Les Fennecs.
Germany will now face France, who beat Nigeria 2-0 in the round of 16, in Rio de Janeiro at the Maracana July 5 in the quarterfinals.
Though Germany enjoyed 78 percent of ball possession and threatened the Algerian backline from time to time, they still failed to score in the regular time.
Meanwhile, Algeria also used quick and simple counter attacks to threaten Germany.
The Algerians were highly motivated for the encounter as the events at the 1982 World Cup were still very much on their mind.
They still felt aggrieved at being cheated out of a place in the second group phase by Germany and Austria's "non-aggression pact" in Spain.
Some Algerians were even calling for revenge for what has become known as the "Shame of Gijon".
In the ninth minute, a long ball sent Islam Slimani behind the German defence. German goalkeeper Manuel Neuer raced out of his area to make up for the defence. Slimani looked to touch past Neuer and shoot but the goalkeeper was able to block his effort.
In the 11th minute, Slimani charged forward again and only had one defender to beat, but Per Mertesacker got a crucial foot in to stop Les Fennecs' attack.
Six minutes later, it was again Slimani whose header found the back of the net but his goal was ruled offside.
After withstanding Algerian attacks, Germany gradually arranged some fightbacks.
On 24 minutes, Mesut Ozil tried to catch Algerian goalkeeper Rais Mbolhi off his line with a chip but the goalkeeper tipped it over the bar. Nine minutes later Thomas Muller's header also went wide.
In the 41st minute when Mario Gotze was alone on goal and got a good look but Mbolhi closed down his space and blocked the shot.
Joachim Loew brought on Andre Schurrle to replace Mario Gotze just after the break. The pace was still flying in the second half as Germany kept the momentum with some quick chances, and Algeria came back on their counter-attack.
In the 55th minute, Philipp Lahm hammered a powerful shot from long distance, but Mbolhi got a fingertip to his blast that looked bound for the top corner.
Germany gradually asserted their dominance afterwards and threatened the Algerian defence from time to time, Algeria also had chance to find a winner, but the excellent performance from goalkeepers of both sides kept the clean sheet in the regular time.