The legendary No.10 scored twice before Alessandro Florenzi put the outcome beyond all doubt with a third goal just before the break, as the visitors maintained their winning run
The veteran forward crafted a beautifully-stuck opener in the 18th minute and, after Ricky Alvarez had rattled the upright for the home side, the Giallorossi legend doubled his tally from the penalty spot.
Kevin Strootman laid on Alessandro Florenzi to crown an excellent counterattack in the final minute of a rampant first-half display to make the points safe.
Federico Balzaretti collected two yellow cards to slightly sour Roma's evening, but their lead at the Serie A summit stands at five points ahead of Napoli's game with Livorno on Sunday, while Inter remain fourth.
The Nerazzurri had made two changes to the side that drew 1-1 at Cagliari last time out - Saphir Taider replacing Mateo Kovacic in midfield and Rodrigo Palacio preferred to Ishak Belfodil in attack. Roma, in contrast, were predictably unchanged from their 5-0 demolition of Bologna.
Having warmed up in commemorative shirts, both sides observed a minute's silence in memory of the victims of the Lampedusa boat tragedy before kick-off.
Roma soon settled into the contest and, following a driving seventh-minute run, Gervinho saw his shot deflected over via a last-ditch challenge from Taider.
Taider was involved at the other end shortly afterwards, taking a touch and drilling a low shot from the edge of the box that Roma goalkeeper Morgan De Sanctis did well to hold low, but Totti would soon show him how it was done from a similar distance.
Florenzi played the ball into Gervinho 20 yards out as he came in from the left and the former Arsenal forward teed up Totti, who smashed home first time to leave Inter goalkeeper Samir Handanovic with no chance.
A superb tackle from Juan Jesus prevented Gervinho from doubling his team's lead in the 24th minute and Inter sprung down the field, allowing Alvarez to send a rasping 25-yarder against the inside of the post with De Sanctis rooted to the spot.
Taider was then wasteful from a couple of set-pieces as the hosts looked to be gaining the upper hand, but they were blown away in a six-minute spell before half-time.
Gervinho proved to be a menace on the right flank once more, dancing past Esteban Cambiasso and drawing a trip from Alvaro Pereira.
The offence arguably took place on the line but the referee pointed to the spot, from where Totti's firmly-struck kick eluded Handanovic's dive.
Roma saved their best until the stroke of the interval, a clever pass from Totti sending Strootman surging at the heart of the Inter defence before a perfectly-weighted ball to his right was clinically crashed into the far corner by Florenzi.
Inter's woes almost increased in the 48th minute when Florenzi was allowed room to turn and hook a volley goalwards inside the area, only to be impressively thwarted by Handanovic.
Walter Mazzarri's men thought they were back in the contest when Palacio flicked on Alvarez's cross for Andrea Ranocchia to beat De Sanctis in an aerial challenge and nod home, but the centre-back was adjudged to have headed the ball out of the keeper's hands.
Gervinho should have added further gloss to the scoreline when he raced clear of a scattered Inter defence to produce a scuffed shot that Handanovic tipped around the post.
Substitute Mauro Icardi almost capitalised on a weak back header from Daniele de Rossi as Inter manfully continued to press - something they did for the rest of the match following Balzaretti's foolish 79th-minute lunge on Alvarez that rules him out of next weekend's mouth-watering top-of-the-table clash with Napoli in the Italian capital.