The north African outsiders played with energy and confidence to regularly expose a static German defence but they were indebted to goalkeeper Rais Mbolhi for a great double save which kept the match scoreless at half-time.
Mbolhi made another excellent save from a close-range Thomas Mueller header to take the match into extra time but the fitter-looking Germans were in control by then and took the lead within 90 seconds of the extra period when substitute Schuerrle cleverly dragged in a low Mueller cross.
Ozil banged in the second in the 120th minute and though Abdelmoumene Djabou replied in added time Germany extended their remarkable record of reaching at least the quarter-finals in every World Cup they have entered since 1938.
It was also Germany's first win in three attempts against Algeria, who famously beat them in a 1982 World Cup group game.
