Andreazzoli, who was placed in charge following the dismissal of Zdenek Zeman earlier in the week, saw the size of the task in hand as Samp showed more hunger and desire to get three points which move them further away from the relegation zone.
Marcelo Estigarribia gave the home side the lead in the 56th minute and Gianluca Sansone doubled their advantage after Roma's Pablo Osvaldo missed a penalty and Erik Lamela had a goal disallowed.
Lamela did reduce the arrears in the 75th minute, but Mauro Icardi sealed the win for the Blucerchiati just two minutes later.
The three points take Sampdoria seven points clear of the drop zone while Roma's hopes of qualifying for Europe next season may now rest on their progress in the Coppa Italia with six points separating them from the top five.
The change in coach appeared to have the desired effect on Roma to begin with as they attacked their hosts.
Lamela was posing a threat in a wide position while Osvaldo was the dangerman in the centre.
Despite their dominance, though, they were unable to create any clear-cut chances while Samp failed to put their leaky defence to the test.
Roma thought they had taken the lead in the 51st minute when Lamela picked his spot in the top left-hand corner of Sergio Romero's goal, but the linesman's flag was raised as Francesco Totti's deflected shot arrived at the Roma forward.
Five minutes later, Sampdoria took the lead when Andrea Poli picked out Estigarribia in space to the left of goal, and he was able to thread a shot past a defender and Maarten Stekelenburg into the far corner.
Roma had the chance to level in the 68th minute when Daniele Gastaldello blocked Osvaldo's path inside the penalty area and the referee pointed to the spot.
Osvaldo stepped up but passed the ball weakly into the arms of Romero.
Instead of being level at 1-1, Roma found themselves 2-0 down moments later when Sansone's direct free-kick found its way through Stekelenburg's hands.
Roma reduced the arrears two minutes later when Alessandro Florenzi's cross took two deflections before being struck in by Lamela from eight yards.
But the game was decided two minutes after when Icardi headed in unmarked from a corner.