Roma seized control from the word go and look set to cruise to victory after Lucas Digne's 23rd-minute opener was followed four minutes later by a second from Radja Nainggolan.
But Atlanta launched a stunning response, Marco D'Alessandro bundling home their first in the 33rd minute then Marco Borriello ensuring they were level before half-time.
Boriello fired his second into the bottom corner five minutes into the second half to give Atlanta a shock lead, and missed a glorious chance to complete his hat-trick.
But in the end it fell to Totti, a 78th-minute replacement for Daniele De Rossi, to steer the ball home and salvage a point which kept the third-spotted Giallorossi in the hunt for an automatic Champions League berth, albeit five points behind Napoli with five games left.
Juventus dispatched Palermo 4-0 to make it seven league wins on the bounce to edge closer to retaining the title.
Sami Khedira's exquisitely taken volley gave the home side the ideal start before Paul Pogba, Juan Cuadrado and Simone Padoin made sure of the victory with second-half goals.
The only downside for Massimiliano Allegri's side came when Claudio Marchisio was carried off on a stretcher with a knee injury after a collision with a Palermo player, sparking fitness concerns with UEFA EURO 2016 looming large on the horizon.
While Juve are on course for a fifth successive title, Palermo continue their slide towards Serie B with a seventh loss in nine Serie A games.
Cristian Brocchi enjoyed a winning start to his stint as AC Milan coach as they ran out 1-0 winners against struggling Sampdoria at the Stadio Luigi Ferraris.
The visitors kept alive their slim hopes of a top-five Serie A finish this season as Carlos Bacca's strike with just less than 20 minutes remaining proved decisive.
Bacca had previously been wasteful, missing a number of clear chances, though he produced the one moment of quality to ensure his dry spell of one goal in eight competitive matches was ended.
Samp, meanwhile, are just six points clear of the drop after Carpi and Frosinone picked up maximum points over the weekend.
Fiorentina kept up their seven-point gap over sixth-place Milan with a 3-1 home win against Sassuolo.
Domenico Berardi cancelled out Gonzalo Rodriguez's opener but Fiorentina retook the lead two minutes later through Josip Ilicic, before Sassuolo goalkeeper Andrea Consigli provided the hosts with their third courtesy of a bizarre own goal.
Simone Inzaghi continued his winning start as Lazio coach as they defeated Empoli 2-0 at the Stadio Olimpico thanks to a Antonio Candreva penalty and a goal from Ogenyi Onazi.
Alessandro Frara was the hero for Frosinone as they responded to Carpi's 4-1 win over Genoa with a much needed 2-1 victory at bottom-placed Hellas Verona.
Meanwhile, Felipe and Riccardo Meggiorini were shown late red cards for Udinese and Chievo respectively as they played out a 0-0 draw at the Stadio Friuli.