After the first 90 minutes ended goalless, Schurrle’s sublime flick broke the deadlock and Ozil doubled the European giants’ lead, with Djabou’s 11th-hour goal proving too little, too late for the spirited north Africans.
The Germans started as overwhelming favourites, but it was Algeria who bossed the opening exchanges. Manuel Neuer vacated his area to attempt to clear a long ball forward, but Islam Slimani’s pace enabled him to get to it just before the Germany goalkeeper and knock it past him down the left.
The 26-year-old striker attempted to stroke it into the unguarded net, but the sliding Neuer was able to clear it out for a corner and spare himself embarrassment.
Slimani then had a header ruled out for offside, before Faouzi Ghoulam latched on to El Arabi Hillel Soudani’s canny through ball and blasted a shot just wide.
Germany’s only chances of the first half came when Adi Mbolhi failed to hold long-range strikes. When Toni Kroos and Mesut Ozil saw their efforts parried, however, Mario Gotze and Thomas Muller failed to capitalise on the rebounds.
The last opportunity of the period fell to Algeria, with Mehdi Mostefa’s goal-bound drive deflecting wide off Jerome Boateng.
Germany, so lethargic in the first half, began the second in top gear. Muller headed straight at Mbolhi from close range, before the Algeria keeper made an acrobatic save to flick a Philipp Lahm strike round the post.
The three-time World Cup winners continued to dominate possession but failed to create any meaningful opportunities, before a brief period of Algerian pressure began on 75 minutes.
Sofiane Feghouli’s flashed a half-volley narrowly wide, Slimani’s piledriver stung Neurer’s hands, and Soudani’s cross was vitally intercepted by Boateng.
Germany regained control and, after Bastian Schweinsteiger had nodded wide, Muller headed straight at Mbolhi from six yards. The Algeria keeper’s parry fell to substitute Andre Schurrle, but his shot was blocked.
Muller then produced two exquisite touches to bring down a long ball and trick his way inside a defender, but he couldn’t do the easiest part and keep his shot on target from nine yards.
The final opening of normal time fell to Schweinsteiger, but the unmarked midfielder’s close-range header lacked power and accuracy.
Germany had missed a series of second-half chances, but Schurrle took their first of extra-time with aplomb.
Muller broke down the left but his cross was a little behind the Chelsea forward. It looked like the chance would pass by, but Schurrle let the ball run through his legs and sublimely flicked it past Mbolhi with his heel.
Germany commanded play thereafter and Ozil thumped home a rebound from close range to make it 2-0 on the stroke of full-time.
Djabou did slot the ball home to give Algeria a glimmer of hope, but they had insufficient time to search for an equaliser.
Vahid Halilhodzic and his charges, who arrived in Brazil as supposed whipping boys, go home with their heads held high.
Joachim Low and his men head to Rio de Janeiro for a Maracana meeting with France.