The former Fiorentina midfielder opened the scoring in the 36th minute but Inter needed a second-half winner from Ivan Perisic as Giampaolo Pazzini would level for Hellas.
Towards the end of an evenly contested first half, Valero opened his account for Inter by steering in Antonio Candreva's cross from close range.
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Inter had chances to double their lead but instead, in the 59th minute, Verona equalised as substitute Pazzini stepped up to convert a penalty after Samir Handanovic had fouled Alessio Cerci.
The hosts' joy was short-lived, however, as Perisic restored Inter's advantage with a 67th-minute goal. Again it was Candreva who provided the assist, which Perisic drove home from the edge of the area.
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