Mattia Destro scored twice, either side of a Miralem Pjanic free-kick, as the capital club overpowered their visitors.
And things got worse for Samp late on as Daniele Gastaldello saw a second yellow card for a careless lunge in the direction of Kevin Strootman.
Roma dominated the play but lacked a cutting edge in the first half, with Gervinho guilty of wasting their best chances as the Ivorian looked hesitant in front of goal.
He had the ball at his feet in the penalty area in the 17th minute but Angelo Da Costa was out quickly to smother the chance - and an even better opportunity came his way just before the half-hour mark.
The Ivorian latched onto a great pass from Strootman to race towards goal on the left-hand side, but his chipped effort over the goalkeeper lacked power and Gastaldello cleared it off the line.
Pjanic fired wide from distance before teeing up Destro for a chance the forward could not convert, and Roma began to grow frustrated as good chances went begging.
Strootman was the guilty party in the 41st minute after Angelo Palombo was caught in possession by Gervinho and played an unforgivable backpass straight to Pjanic. He slid it to Strootman but the Dutchman's shot was weak and straight at Da Costa.
Their frustration turned on the officials moments later when Strootman threaded it through to Gervinho but the Ivorian again hesitated and was tackled. Destro tried to pick up the pieces but was thwarted by what looked a handball.
However, all was forgotten as Destro headed in the resulting corner.
The one-way traffic continued in the second half and Roma fans were still celebrating Pjanic's free-kick - a straight shot which went through a crumbling wall - when Destro blasted in the third after 57 minutes, turning his defender before firing into the roof of the net from close range.
Samp were being run ragged and Gervinho tested Da Costa again before Nenad Krsticic blocked Strootman's shot.
Gastaldello was responsible for the final indignity with a needless lunge at Strootman in midfield, not even making contact but more than earning his second yellow card.