Alessandro Florenzi headed the visitors into a lead with a quarter of an hour gone only for Antonio Cassano to restore parity on the stroke of half-time.
Both sides had chances in an even opening to the second period before Pablo Daniel Osvaldo restored Roma’s advantage.
Osvaldo then turned provider as Marquinho made sure of all three points with a volley from a tight angle with a little under ten minutes remaining.
Although Osvaldo finished the game with a goal and an assist, Totti was the game’s stand out player with an assist either side of half-time enough to ensure all three points went to the men from Rome.
Having comfortably beaten Pescara 3-0 last weekend, Andrea Stramaccioni’s side faced an early test of their title credentials against Zdenek Zeman’s Roma at the San Siro without first choice goalkeeper Samir Handanovic.
Roma, also tipped to challenge Juventus for the Scudetto, began with a disappointing draw 2-2 against Catania, a performance that Zeman, in his second stint at the club, described as containing ‘pointless’ passing.
Zeman’s side responded to that criticism with verve as they dictated much of the early play with talisman Totti at the fulcrum of nearly every move.
And it was Totti who produced a near perfect ball for Alessandro Florenzi to steal in and head past Luca Castellazzi in the home goal to give the visitors the lead with a quarter of an hour gone.
The visitors were playing with a three pronged attack and the ease with which Totti was finding space during the early exchanges will have been a worry to Stramaccioni, but, bar that early strike, Roma failed to capitalise on the space offered to them.
The loss of Daniele De Rossi to injury with a little over half an hour gone further disrupted the visitors’ fluency as Inter began to take a foothold in midfield, but, despite their territorial superiority, the hosts had only one clear cut opportunity to speak of as the game edged towards half-time.
That was a Diego Milito header that just flew past the wrong side of the post from close range but as it looked like the men from Rome would be going to the interval with the slenderest of advantages, Cassano broke the offside trap to receive Wesley Sneijder’s clipped through ball with his back to goal.
The former Roma man worked some space, and, although his shot was firmly hit, it was a pretty rudimentary save for Maarten Stekelenburg until a deflection reduced the Dutch keeper to the role of spectator as the effort looped up and into the far corner to ensure the teams went to the break at parity.
Having lost the initiative as the first-half drew to a close, Roma regained it with some intent in the opening exchanges of the second period and would have been in the lead had it not been for some errant Osvaldo finishing.
Having stumbled upon a gaping hole in the middle of the Nerazzurri defence, the forward lost his bearings with his back to goal and hooked an effort high and wide with only the keeper to beat before snatching at a volley from close range.
Inter were carving out chances of their own, the best of which fell to Guarin but his touch let him down and he was forced wide. The shot, from a tighter angle than it needed to be, was easily charged down; minutes later he cut inside and drew a save from Stekelenburg from outside the box.
The rise of Inter coincided with Totti’s loss of influence on the game but Roma’s talisman found a pass of rare quality for Osvaldo to capitalise on a slip by Matías Silvestre to run clear on goal and lift the ball over the onrushing Castellazzi to reclaim the lead.
As Inter chased an equaliser, they left gaps at the back, one of which was exploited by a well-timed Marquinho run as Osvaldo turned provider with an inch perfect ball with the outside of his boot from the left.
The substitute did extremely well to take the ball down on the run before squeezing a sweetly struck volley between Castellazzi and the post to put his side into an unassailable lead.
Second-half goals from Marek Hamsik and Blerim Dzemaili gave Napoli a 2-1 win over Fiorentina on a San Paolo pitch which was heavily sanded, full of ruts and divots and appeared to be nearly unplayable. Stevan Jovetic replied for the visitors.
Germany striker Miroslav Klose scored twice to guide Lazio to a 3-0 win over Palermo.
Cagliari's supporters missed out on a dramatic finale as Albin Ekdal's stoppage-time goal gave them a 1-1 draw with Atalanta, who had taken an 81st-minute lead through German Denis.
Cagliari had played at the Stade Sant'Elia from 1970 until around halfway through last season but abandoned the arena due to disagreements with the local authorities and over growing safety worries.
The Is Arenas stadium outside Cagliari was only confirmed as the venue on Friday night after the home players protested at plans to stage the match in Trieste, around 1,000 kilometres away on the mainland.
Cagliari, who hosted several matches in Trieste last season, were not allowed any spectators with one half of the arena still clearly under reconstruction.
Elsewhere, Catania defeated Genoa 3-2, Sampdoria saw off Siena 2-1 and Parma won 2-0 against Chievo in home wins.