A five-minute sequence at the death saw the Spaniard and Ryder Matos overturn proceedings and book the Italian side's place in the next round.
An astonishing goal from Brazilian Eric Pereira put the home side ahead 32 minutes in as he met a cross from the left with a looping overhead volley that dropped into the top corner.
Pandurii briefly pushed for a second, with Pereira coming close again in the first half. Although the visitors bossed the majority of proceedings, they were continually thwarted by a rigid back line and substitute goalkeeper Pedro Mingote.
However, just as la Viola looked destined for a shock defeat against a side with only one point from its opening three matches, the game was turned on its head.
Juan Cuadrado, who had earlier spurned excellent chances for an equalizer, raced away down the right and fizzed in a cross allowing Matos to tap home from close range. Matos then thought he had stolen all three points, only for a dubious offside call to rob him of a second.
However, deep into injury time, Colombian Cuadrado once more supplied the telling ball from the right to find Valero unmakred in the area, and the Spaniard squeezed his effort over the line to put Vincenzo Montella's side into the next round, with four wins from its first four matches.