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Inter struggled to create any goalscoring opportunities before Saphir Taider came close with a volleyed effort from the edge of the box that sailed just wide.
Inter took the lead with four minutes of the first half left as Marco Andreolli smashed home a loose ball from inside the box following Chievo's failure to clear a free kick.
In the second half Chievo looked for a way back into the game and they drew level in the 73rd minute. Lazarevic played in Obinna down the left-hand side of the box before the striker lashed a fierce strike past Carrizo.
In the final minute of the match Chievo stole all three points as Obinna fired in a shot from range that beat the keeper and found the bottom corner.