Roma finished the match with 10 men after defender Federico Balzaretti saw red for a second rash challenge of the game in the final 10 minutes, but by then the damage had been done.
Totti struck a sweet opening goal in the 18th minute when he drove Gervinho's lay-off past a static Inter defence and beyond Samir Handanovic in the Inter net.
Roma won a controversial penalty five minutes from half-time and Totti stepped up to double the visitors' lead.
Roma's seventh win in as many games means Rudi Garcia's men have stretched their lead over Napoli and Juventus to five points ahead of their respective matches against Livorno and AC Milan on Sunday.
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Although Roma remain in pole position, club captain Totti was careful not to make mention of the scudetto: "It's been an amazing start to the season.
"This squad can go far and although the season is long and we will come up against teams that are stronger than us we have to fight for a Champions League place.
Inter's first defeat of the season under new coach Walter Mazzarri leaves them in fourth, now seven points off the pace.
On account of some positive displays since the start of the season, and an attack that was second only to Roma's, Inter had been expected to offer a stiffer challenge.