The hosts enjoyed a near-perfect start on Tuesday as Sergio Aguero won and converted an early penalty before familiar frailties in Europe's premier competition came to light for City.
Their defence was rarely allowed to settle as Roma produced superb attacking movement and took complete control of midfield, with Miralem Pjanic to the fore.
The Bosnia international supplied the ammunition for Totti to find a 23rd-minute leveller with a brilliant finish, taking the record from crosstown Manchester hero Ryan Giggs three days on from his 38th birthday.
Although Roma failed to recreate their first-half dominance after the break, the draw does far more favours for them in the wake of an opening 5-1 victory over CSKA Moscow.
The Russian champions are up next for City, who are winless in two outings and yet to score from open play.
As expected, Joe Hart returned in goal for City in place of Willy Caballero after two games on the bench, while there was also a change in goal for Roma as Morgan De Sanctis (groin) failed a late fitness test to hand Lukasz Skorupski a rare start.
Experienced City centre-back Martin Demichelis replaced Eliaquim Mangala following the latter's shaky showing in Saturday’s 4-2 win over Hull City, facing up a Roma attack featuring Totti, Gervinho and Alessandro Florenzi.
Roma right-back Maicon returned to face his former club and displayed the inauspicious form on show all to often during his season at the Etihad Stadium when he hauled back Aguero to concede a fourth-minute penalty.
Aguero coolly converted but Maicon almost made amends at the other end when he flashed a venomous strike against the underside of the crossbar after Totti's delicate chip had unlocked the City defence.
That close call appeared to rob City of their early poise and Hart was out sharply in the 18th minute after Gervinho had evaded Vincent Kompany, before the equaliser arrived from a familiar source.
Totti spun in behind Kompany to collect a perfectly weighted pass from the excellent Pjanic and lifted a superb finish over Hart.
Roma were fortunate not to concede a second penalty when a prone Kostas Manolas blocked Jesus Navas' cutback with his outstretched arm, but the visitors almost led after 43 minutes when Gervinho raced beyond Gael Clichy and Demichelis to draw a fine save from Hart.
James Milner replaced Navas at half-time as Manuel Pellegrini sought to stem Roma's midfield dominance, but Hart was again the goalkeeper in action seven minutes after the restart.
Florenzi's cross struck a flat-footed Demichelis and fell invitingly for Pjanic, with Hart spreading himself effectively.
Pjanic then arched a curling 25-yard effort narrowly wide as City laboured, despite Milner injecting energy to proceedings.
City midfielder Fernandinho exchanged passes with Yaya Toure and the recently introduced Frank Lampard to prompt a vital last-ditch challenge from Mapou Yanga-Mbiwa in the 60th minute.
Five minutes later, Pjanic lashed a shot over from the edge of the area - a moment of wastefulness out of keeping with his all-round display - before Skorupski got down well to his left to stop Lampard continuing a purple patch in front of goal.
David Silva prodded the ball narrowly wide from Pablo Zabaleta's stoppage-time centre, but City have plenty to do if they are to avoid a third group-stage exit in four seasons.
