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Miralem Pjanic came close to giving Roma the lead from a corner on five minutes, but his header was just off target.
Francesco Totti showed superb balance to create a chance on goal after 22 minutes, but the veteran could not find the finish.
Andrea Costa had an attempt for Sampdoria early in the second half, but just missed the target as the home side pushed forward.
Roma were given the chance to get back into the game when the referee awarded them a penalty on 68 minutes. Osvaldo stepped up but saw his spot kick saved by Sergio Romero.
Sansone then dealt a blow to Roma's chances of getting anything from the game, doubling the home side's lead on 73 minutes.
Roma got themselves right back into the game two minutes later when Erik Lamela struck to make it 2-1.
Sampdoria went straight on the attack and restored their two-goal advantage on 77 minutes through a Mauro Icardi header.