The 36-year-old needed one more goal to match former AC Milan striker Gunnar Nordahl's career haul of 225 goals, and that goal arrived from the penalty spot with 15 minutes on the clock.
Genoa battled hard to spoil Totti's night, though, and Marco Borriello ensured the second half would be a contest by converting a spot-kick of his own, against his former club, just before the break.
Teenage defender Alessandro Romagnoli then took his first step towards chasing Totti's goal record with his maiden league goal and Simone Perrotta put the result beyond doubt after Juraj Kucka was dismissed following an angry exchange with Totti.
The three points guide resurgent Roma into seventh place under new coach Aurelio Andreazzoli while Genoa remain perilously close to the relegation zone, with only a five-point cushion protecting them from Siena, Palermo and Pescara.
Kucka's speculative shot from distance demonstrated some of the new verve that surrounds Genoa and the Slovakian went close once again with another fierce drive in the opening exchanges.
Pablo Osvaldo was unlucky not to connect with Vasilis Torosidis' defence-splitting pass before Luca Antonelli cut out a Totti through-ball to his Greek team-mate.
De Rossi tried to go it alone in the 15th minute and, although his jinking run did not produce a goal, a heavy-handed Genoa back line saw Roma presented with an opportunity to take the lead.
The stage was set for Totti to make history from the spot and he did not disappoint, steering his 225th Serie A goal underneath the outstretched glove of Sebastian Frey.
Genoa were unmoved by Totti's moment of glory and soon began to dominate the final third, winning a remarkable 11 corners in a tense 20-minute period.
The best chance would fall to Andrea Bertolacci, whose header forced Maarten Stekelenburg into a fine save, but Genoa could just not outmuscle their hosts in the air.
Three minutes before the break Genoa forced their way back into the game as Borriello won a penalty from Nicolas Burdisso on the edge of the box.
There was no overt celebration from the former Roma striker as he tucked the ball beyond Stekelenburg, but Borriello did welcome his team-mates into a group hug.
Roma were the brighter side following the restart, though, and Erik Lamela went desperately close to his 12th goal of the season only for Emiliano Moretti to close him down in the six-yard box.
Frey played a big part as the Giallorossi edged ahead once again in the 58th minute, rushing carelessly off his line and watching in horror as Romagnoli headed into an empty net.
That single action caused chaos at both ends, with Stekelenburg denying Bertolacci with a flying save after Osvaldo and Totti had both worried Frey with searing strikes.
Tensions flared and Ballardini was sent to stands for demanding a stoppage in play when Daniele Portanova clashed heavily with Osvaldo in the area, and Kucka and Totti were soon found arguing about the incident in the middle of the pitch.
The Italian veteran was booked for his role in the scuffle but Kucka earned a second yellow card and his marching orders at the Stadio Olimpico.
From that point it appeared the game would peter out to a tame conclusion but there was still enough time for Perrotta to slide in and scoop the ball home with two minutes left to play.