Roma were looking to register consecutive league wins for the first time since mid-January, though their chances were dealt a blow with exactly a minute played.
Marcus Thuram chased a Manuel Akanji ball down the right and squared for Lautaro Martínez, who got across his marker and fired the Nerazzurri ahead.
Mile Svilar stood no chance with the finish, though he fared better with strikes from Hakan Calhanoglu and another from Martínez to prevent his side’s poor start from becoming disastrous.
The visitors eventually gained a foothold on the match and came close to a leveller midway through the first half, when Yann Sommer appeared to defy physics when diving to claw away Donyell Malen’s header following a free-kick.
Malen had another strike from range whistle just wide soon after, and that was the only clear chance for either team until Gian Piero Gasperini’s side drew level five minutes before the break.
Devyne Rensch collected Matias Soule's pass down the left and clipped an inviting cross for Gianluca Mancini to head home.
However, parity only lasted until the stroke of half time, when Çalhanoglu took aim from over 30 yards out and sent a rocket past the diving Svilar to put the home side back in front.
That goal swung the momentum back in Inter’s favour, and they made it count with two more in the first 10 minutes of the second half.
First, Thuram won an aerial battle with Rensch that set up a three-on-two, allowing the Frenchman to again combine with Martínez, who slotted home his second of the night.
Then it was Thuram’s turn to get in on the act, as he leapt highest to flick Calhanoglu’s corner beyond Sommer.
Just after the hour mark, Nicolo Barella picked up a loose ball and attempted to set up Thuram for another, but when his pass ricocheted back into his path, the Roma defence opened up for Barella to go through and score number five.
The visitors added some respectability 20 minutes from time when Lorenzo Pellegrini finished well after Malen had stretched the Inter defence, though Denzel Dumfries missed a golden chance to add further humiliation, before Svilar reacted well to deny Pio Esposito.
It’s now 10 wins in the last 12 H2Hs for Cristian Chivu’s side, while the Giallorossi are winless in five on their Serie A travels.
Flashscore Man of the Match: Marcus Thuram (Inter Milan)