The hosts shrugged off their poor league form - which has seen them go five games without a win to slump to 19th in Serie A - to gain a measure of revenge for October's 2-0 league loss to the same opponents.
Gianluca Sansone set Samp on their way with a well-taken volley after 15 minutes, and they doubled their advantage just five minutes later courtesy of Birkir Bjarnason's opportunistic strike after goalkeeper Nikolay Mihaylov had parried a shot.
Head coach Sinisa Mihajlovic drew his first two games in charge and saw his side begin to relinquish their dominance as Samuele Longo shot wide and Daniele Cacia headed over before the break.
Verona's resurgence looked to have been blunted after a low-key start to the second half but Longo supplied an excellent finish from Raphael Martinho's cross to set up a potentially nervy final 25 minutes.
The visitors' push for a leveller saw coach Andrea Mandorlini introduce veteran striker Luca Toni from the bench and Verona piled on the pressure, but Nenad Krsticic and Renan Garcia scored in the final seven minutes to put the result beyond doubt.
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