Lazio's Luis Alberto scores during a Serie A soccer match between Lazio and Roma
Aleksandar Kolarov's 17th-minute penalty put Roma ahead amid a flurry of chances with Lazio hitting the post three times and Roma twice inside the opening half hour.
Simone Inzaghi's side looked the more threatening and levelled on the hour mark through Alberto's strike.
But they were denied by the frame of the goal again when substitute Marco Parolo hit the crossbar late on, before Manuel Lazzari thought he'd scored the winner in stoppage-time, only for the effort to be ruled out for offside in the build-up.
"It was a spectacular Rome Derby," Roma coach Paulo Fonseca told Sky Sport Italia.
"Coaches always lose a few years of life during games like this, but this was an anthem for football to those who love the sport."
Fonseca's counterpart Simone Inzaghi wasn't quite as upbeat after seeing his side squander golden opportunities to take all three points. "Considering the game overall, there is real regret and disappointment, because we had 21 shots on goal and hit the woodwork four times," he said.
"There are inevitably regrets, because we had so many chances and you have to win games like that."
The fixture, one of Italy's most ferocious rivalries, had never been held in the opening two weeks of the season before and the sides came into the game in contrasting spirits after Lazio comfortably beat Sampdoria 3-0 and Roma were held to a 3-3 draw by Genoa.
Lazio midfielder Lucas Leiva's volley came back off the post after three minutes before Roma's Nicolo Zaniolo struck a shot off the upright.
Roma broke the deadlock when Sergej Milinkovic-Savic was pinged for handball and Kolarov stepped up to send goalkeeper Thomas Strakosha the wrong way from the spot.
As astonishing period of play followed in front of a raucous crowd as Lazio strikers Ciro Immobile and Joaquin Correa hit the woodwork within a minute of each other before Zaniolo struck another shot off the post two minutes later.
Lazio continued to press for an equaliser after the break and were rewarded when Immobile laid a pass into the path of Alberto, who smashed a shot past Pau Lopez to level the scores.
Inzaghi's side were not content to settle for a draw and came agonisingly close to taking maximum points when Parolo curled a shot off the crossbar with five minutes remaining before Lazzari's stoppage-time goal was ruled out for offside.
Parolo's effort marked the sixth time the woodwork rattled during the match, setting a new Serie A record since Opta began gathering statistics in the 2004-05 season.
The result left Lazio on four points ahead of their trip to SPAL after the international break and Roma have picked up two points from their opening two games and host Sassuolo next.