The Premier League outfit started the afternoon brightly, taking the lead with just 10 minutes on the clock courtesy of a 30-yard screamer from Steve Sidwell.
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Highly-rated teenager Mesca had an opportunity to double their lead seven minutes later, collecting a pass from Byran Ruiz in the danger zone, but he shot straight at Parma goalkeeper Antonio Mirante.
Parma had the ball in the net in the 23rd minute, but the goal was rightly ruled out for an offside against Italy international Amauri.
Both sides had opportunities late, with Ruiz landing a free kick on the roof of the net and Stefano Okaka heading over unmarked at the other.
However, it was Parma who dug deepest ahead of the final whistle, finding a winner as Sansone headed in Gianni Munari's cut-back at the far post with four minutes remaining.