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Mbaye doubled his side's lead eight minutes later when he latched onto Marco Benassi's cross and slotted home from inside the six-yard box.
The home side continued to press forward and in the 53rd minute they levelled the score. Federico Ceccherini tried to put the ball behind for a corner, but he could only divert it into his own net.
Sampdoria were in control of the match and Soriano came close to a third when he drilled an effort into the side-netting from a tight angle.
In the 68th minute the hosts took the lead. Stefano Okaka fired in a strike from long range that took a slight deflection of Andrea Coda and left Francesco Bardi helpless, as it found the back of the net.
Manolo Gabbiadini soon made it four as he latched onto a through-ball from Okaka, before lashing an effort past Bardi.