The hosts dominated from the off but were initially thwarted by Kenan Bajric, who made a double block to deny Donyell Malen and Niccolo Pisilli before also blocking a Lorenzo Pellegrini attempt.
Pellegrini then smashed a strike over the crossbar but was involved in the opener, which arrived in the 22nd minute, as he won and delivered the free-kick that Daniele Ghilardi met to head it back across goal for Mario Hermoso to nod it in at the back post.
Pellegrini’s personal quest for a goal continued when Dominik Takac saved a curling effort, before Gian Piero Gasperini’s wing-backs linked up and Nahuel Molina struck wide from a Wesley Franca cross.
Molina had his goal in the 39th minute, though, as the Argentine finished after Takac had palmed Malen’s attempt into his path.
Malen had more chances after the restart, but Takac read his attempt to loop the ball over Slovan’s goalkeeper, and the Dutchman made a mess of his volley from a corner.
Malen still played a part in punishing Tigran Barseghyan after Matias Soule stopped him from letting the ball run out of play, laying it off for Pisilli to finish.
The visitors’ evening quickly got worse as Cesar Blackman desperately tried to track Wesley but brought him down, conceding a penalty that Malen clinically sent into the bottom corner.
The hosts’ comfort was encapsulated by Wesley and Malen both being brought off immediately after the penalty they contributed, even with just 59 minutes on the clock.
Santiago Castro struck off-target shortly after his introduction, before Ghilardi saw a header saved, Molina volleyed wide, and Takac impressively denied Rodrigo Mora.
The hosts continued coming forward, but there wasn’t to be a fifth as Ghilardi’s strike was ruled out due to his teammates being offside, but there won’t be any complaints with Roma recording back-to-back wins across all competitions, which means the defeat to Real Madrid is still their only loss this term.
The Giallorossi’s first Champions League win this season keeps Slovan Bratislava bottom of the table, having conceded 13 goals in three matches while scoring just one.
Flashscore Man of the Match: Niccolo Pisilli (AS Roma)