The German forward opened the scoring in the opening stages and Antonio Candreva sealed three points for the Romans, while Murillo saw red on a nightmare day for the away team
An early Miroslav Klose strike put Lazio on the path to a 2-0 victory over Inter on Sunday, ending the visitors’ hopes of making the Champions League in the process.
Roberto Mancini’s side needed a win to keep the pressure on third-placed Roma in Serie A, but Miroslav Klose’s eighth-minute goal set them back in the capital.
Inter turned on the style to put three goals past Udinese last time out but they were sluggish and short of ideas against Lazio, with Ivan Perisic and Stevan Jovetic coming closest to finding an equaliser.
Lazio were likewise unadventurous in attack once they had their advantage, although Keita Balde felt aggrieved to be booked for simulation rather than see a penalty awarded midway through the second period.
Inter turned up the heat a little late on but an equaliser never looked likely to materialise, and Antonio Candreva settled the contest seven minutes from time from the penalty spot after Jeison Murillo earned a second booking for felling Keita.
The result means Juventus, Napoli and Roma are now assured of finishing in the Champions League places this season.
Lazio may have little but a top-half finish to play for, but they seized the initiative early on. Senad Lulic slipped the ball through to Klose, who waited for Samir Handanovic to go to ground before lifting the ball expertly into the net from point-blank range.
Inter looked unsettled by the early goal but almost snatched an equaliser when Geoffrey Kondogbia chipped a fine pass to Jovetic, who was denied by a sprawling save from Federico Marchetti.
Candreva stung the fingertips of Handanovic from 30 yards, and the Slovenian saved superbly moments later as Keita burst into the area and aimed a low shot at the far corner.
Inter showed something of an improvement early in the second half but Lazio were frustrated not to be given a chance to extend their lead when Keita was booked for diving after going to ground under pressure from Miranda in the penalty area.
Roberto Mancini introduced Jonathan Biabiany for Gary Medel in an effort to give more support to the frustrated Mauro Icardi in attack, but too often the final pass let them down as Lazio looked content to sit deeper and hit on the break.
Perisic dragged a promising opening wide of Marchetti’s left-hand post before Jovetic came within inches of prodding home following a corner, as Inter at last began to apply consistent pressure with 20 minutes to play.
Perisic tested Marchetti with a decent free-kick and Miranda turned Marcelo Brozovic’s resulting corner over the bar, but that was as good as it got for the visitors in attack.
Keita finally earned a spot-kick as he twisted and turned away from Murillo, who was given a second yellow card for the foul, and Candreva picked out the top corner from 12 yards to seal the win which means Inter must now focus on securing a Europa League spot.