Eric Bailly played the full 90 minutes for the Elephants, while Amad was introduced from the bench just before the hour mark, as the African side held the 2016 runners-up, knocking them out of the competition in the process.
Benjamin Henrichs's own goal gave Ivory Coast a brief lead, before Eduard Loewen's equaliser, but Bailly and co held firm to prevent the Germans finding another goal, ensuring that Soualiho Haidara's men qualify in second place behind holders Brazil.
They will now face Spain at 09:00 BST in Saturday's quarter-final, with the match to be played at the Miyagi Stadium in Rifu.