Cyril Thereau should have given the home side an early lead, but his low drive from close range was pushed wide by the keeper.
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The visitors soon made them pay for that miss and took the lead when Eder headed home a corner kick.
Manolo Gabbiadini came close to doubling their advantage, but after going past two defenders, he fired a strike over the bar.
In the final minute of the game, Sergio Pellissier wasted a big chance to score for the hosts when he headed wide, as Sampdoria held on to claim the three points.