Rudi Garcia's men had fallen 14 points behind leaders Juventus thanks to a run of four straight draws in the league prior to Monday's clash.
De Silvestri and Muriel struck in the second half of a game Roma largely dominated to inflict a rare home defeat, with Seydou Keita's needless dismissal and subsequent refusal to leave the pitch further souring the evening.
Garcia's men had made most of the early running, although Sampdoria produced a rare breakaway 10 minutes in, which resulted in Vasilis Torosidis being forced to clear De Silvestri's dangerous delivery.
Keita thought he had opened the scoring when he converted Alessandro Florenzi's 18th-minute free-kick, only to see his joy cut short by an offside flag.
Gervinho set up Juan Iturbe before the half hour but the Argentinean was denied by Emiliano Viviano, with the Sampdoria goalkeeper stopping a potential Vasco Regini own goal and a Gervinho strike before the break.
The onslaught continued in the second half as Francesco Totti failed to divert Florenzi's cross home with Keita perhaps in a better position behind him.
However, 14 minutes into the second half, De Silvestri's persistence saw him snaffle up a loose ball inside the area to punish slack defending.
Much of the praise should go to Alessio Romagnoli down the left and, while Roma pressed in search of an equaliser, they were again undone by a quick counter 12 minutes from time.
Muriel burst down the left and saw his effort hit the post but after Eder meandered into the box with the rebound, the ball fell kindly for Muriel who tucked away the decisive second.
Roma's outing went from bad to worse when Keita was dismissed - the former Barcelona man sarcastically applauding the referee having been booked seconds earlier for a tangle at a set-piece.
Keita refused to leave the pitch initially, loitering behind the goal, before a member of the backroom staff had to remove the Malian from the pitch.
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