Club captain Totti scored twice inside the opening eight minutes, while Fabio Borini, Juan and Miralem Pjanic scored the other goals, with Eder netting for Cesena, who remained rooted in the bottom three.
It meant the 35-year-old reached 211 top-flight league goals for the capital club, surpassing the 210 that Swedish great Gunnar Nordahl managed for AC Milan more than 50 years ago.
“It’s what I’ve always wanted, to wear this shirt and beat one record after another,” said Totti.
“I feel good, I’m going to enjoy this splendid moment and I will keep playing as long as I’m physically able to do what I want to do and if that’s no longer the case, I’ll be the first to stop.”
Totti’s coach Luis Enrique also paid tribute to the emblematic forward.
“Everyone knows that Francesco is a player with different qualities. Today he scored two goals and played a great match,” said the Spaniard.
“The numbers speak for themselves. He’s a great player and he still wants to be a point of reference for the team.”
Sixth-placed Roma are now just eight points off top spot after the same number of games as the teams above them.
At times they were on another planet to their visitors.
“This type of football doesn’t just please me but would please any coach,” added Enrique. “If the players enjoy themselves, they have a better chance of winning.
“Everything seemed easy today because we were almost perfect in the beginning but Cesena are an excellent side. The result was such because we were on a very high level.”
Totti feels Roma are capable of more than just a battle for Europe this season.
“If we play like this we can go a long way. We’re enjoying it and we’re making it fun for the fans,” he said.
“I think the secret in this jump in quality is the possession football and instinct to get forward that Luis Enrique has instilled in us.”
The match was all over inside eight minutes as Roma swept into a three-goal lead, carving through Cesena’s porous defence.
After Gabriel Heinze’s raking cross-field ball, Totti took a backheel from Erik Lamela after just 40 seconds and fired home at Francesco Antonioli’s near post thanks to a deflection off Maurizio Lauro.
And then on eight minutes he was there at the back post — although television replays showed he was offside — to volley home Lamela’s cross from the left.
Before the eighth minute was up, Gianluca Comotto was caught in possession and Totti released Leandro Greco down the left to cross for Borini to tap home.
It could have been much worse for Cesena in a first half in which they were chasing shadows.
Pjanic, Borini, Fernando Gago, Rodrigo Taddei and Aleandro Rosi all had chances that were either blocked or went wide as Cesena held on by their finger-nails.
In the second period, Cesena briefly rallied when Brazilian Eder skipped between defenders Heinze and Taddei onto a through ball, chipped goalkeeper Maarten Stekelenburg and shot home on 58 minutes.
But just three minutes later, Borini headed a corner goalwards that Antonioli tipped onto the post only for Juan to slot home the loose ball from close range.
Pjanic rounded off the scoring 20 minutes from time as he strode forward and hit a shot that was too hot for Antonioli to handle.
While Cesena’s defence ball-watched, the Bosnia international darted onto the loose ball and knocked it in.
Spanish substitute Bojan Krkic could have added gloss to the scoreline after a mazy dribble beating four players in the box late on but Antonioli tipped his finish over.