Fabio Simplicio scored the winner with 13 minutes to go when he picked the ball up following a mazy run from Jeremy Menez and calmly slotted home from just inside the box.
After a gritty opening period shaded by Lazio, the game burst into life with two penalties in the first 12 minutes of the second half.
Roma took the lead on 53 minutes when striker Marco Borriello converted after Stephan Lichtsteiner handled John Arne Riise's volleyed cross.
Four minutes later, Roma's Brazilian defender Juan brought down Mauro Zarate and midfielder Hernanes sent Julio Sergio the wrong way to equalise from the spot.
Mauricio Isla's last-minute strike cancelled out Samp striker Federico Macheda's opener on 31 minutes in a 90 minutes the home side had dominated.
In a shootout that swung one way and then the other, Sampdoria left-back Reto Ziegler blasted the eighth penalty over before Junior Costa saved Denis's kick.
