The relegation-threatened visitors were kept in it through third-choice goalkeeper Nicola Ravaglia before the break, while Georginio Wijnaldum was denied by the woodwork.
But the Dutchman headed home after Jeison Murillo was shown a second yellow card early in the second half and the three points were wrapped up late on through a Paulo Dybala penalty and Stephan El Shaarawy strike, sending Roma into fourth and level on 50 points with Inter above them.
Red card opens the door for AS Roma
Samp coach Dejan Stankovic, up against his former Inter treble-winning mentor Mourinho, was left furious by the red card decision as his side suffered a defeat that leaves them looking doomed, sitting second-bottom and 10 points from safety.
Mourinho switched to a back four for the first time since January 2022, his hand forced by the absence of suspended centre-backs Roger Ibanez, Marash Kumbulla and Gianluca Mancini, while Tammy Abraham was restored up front after being benched for the 1-0 defeat to Lazio last time out.
El Shaarawy had a couple of sniffs early on before Dybala dribbled a tame shot wide, but Samp grew into the game and produced some testers for Rui Patricio through Mickael Cuisance and Manolo Gabbiadini.
With the rain thundering down and three yellow cards being flashed in the opening quarter it wasn’t the slickest of games to watch, but Roma soon began to pile on the pressure, only to be denied by unlikely hero Ravaglia.
The Samp keeper was making his first start for the club more than two-and-a-half years after joining, with Emil Audero and Martin Turk unavailable, but there were no signs of rust when he sprung to his right to tip away a dangerous Diego Llorente header.
Wijnaldum proves vital
Wijnaldum hared after a through ball and got a shot away on the stretch but it cannoned off the far post, and the home crowd groaned in frustration when Ravaglia pulled off a sharp double-save to deny Nicola Zalewski and Lorenzo Pellegrini and keep his side level at the break.
Murillo’s expulsion in the 52nd minute for a late challenge on Abraham left his side up against it, and Roma quickly took advantage of the extra man when Wijnaldum ghosted in to head home a Nemanja Matic cross from close range.
Dybala whipped a dangerous shot just wide of the top corner and Spinazzola had a shot palmed wide.
The game was put to bed in the 88th minute through Dybala’s penalty, awarded after a trip on Wijnaldum by Ravaglia, and El Shaarawy finished well into the bottom corner in stoppage time as the hosts finished with a flourish.