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.
Striker Silvio Piola - the 1938 World Cup winner who played for Pro Vercelli, Lazio, Torino, Juventus and Novara from 1929-54 - leads the all-time list with a seemingly insurmountable 274 goals.
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 remains perilously close to the relegation zone, with only a five-point cushion protecting them from Siena, Palermo and Pescara.
Rodrigo Palacio came off the bench to score a brace including an injury-time winner in a 3-2 win over feisty Catania to push Inter Milan up to fourth in Italy Serie A.
Inter is one of several teams vying for the coveted European places, having missed out on the UEFA Champions League this season.
But it looked to be heading for yet another setback until Palacio sealed Inter's 14th win of the campaign with a textbook goal in the second minute of injury-time.
Inter started what was always going to be a tricky away fixture in Sicily, where seventh-placed Catania has an impressive home record, without striker Antonio Cassano after his recent bust-up with coach Andrea Stramaccioni.
As expected, the visitor was given short shrift by the Sicilians and was left playing catch-up inside 10 minutes when Gonzalo Bergessio smashed the ball past keeper Samir Handanovic after a defensive blunder by Brazilian defender Juan Jesus.
Inter was in disarray and went in at halftime two goals down after Giovanni Marchese doubled the lead with a header at the back post from Francesco Lodi's free kick.
When Fredy Guarin's angled drive flashed past the Catania post it signalled the visitor's comeback.
Minutes later Palacio latched onto Ezequiel Schelotto's through ball, took it to the byline and sent over a cross for Ricky Alvarez to beat Mariano Andujar from close range with a diving header.
Catania was then left lamenting a missed opportunity when Palacio, who was unmarked in the box, rose above Alexis Rolin to head home Alvaro Pereira's cross from close range.
Catania's defence were found wanting in the second minute of injury time when Palacio was allowed space on the edge of the area and found fellow Argentine Esteban Cambiasso.
Cambiasso took the ball to the byline and squeezed it to the unmarked Palacio, who beat Andujar with ease from metres out.
Elsewhere on Sunday, Fiorentina held onto sixth place, 14 points behind Juventus but only three shy of third-placed Milan, with a 2-1 home win over Chievo thanks to Larrondo's 78th-minute header.
Bologna climbed further away from the relegation zone towards mid-table respectability with a 3-0 home rout of Cagliari, while Sampdoria had Emanuel Icardi to thank for the 58th-minute header which secured a 1-0 win over Parma.
At Siena, Giacomo Bonaventura scored a brace for Atalanta to secure a precious 2-0 away win. Sunday's early match between Torino and Palermo finished scoreless.