The Viola now have 12 points from their first seven fixtures - one more than the capital side - but have only won once in their last five league games, having been victorious in their opening two fixtures.
After the game, coach Vincenzo Montella admitted his side had been fortunate to deny Lazio all three points and said the international break had come at a good time given his side's stuttering form and injury concerns.
"It is an important result and we take the point, even if Lazio did more and deserved something more," he told Sky Sport Italia after the game.
"We tried to take the initiative, but we weren’t sharp enough tonight. The result is positive, because last season we wouldn’t even have managed that with this performance.
"The break comes at the right time, as we can get some players back from injury and rest others who haven’t had the chance. It’s no coincidence we lacked sharpness this evening."
Elsewhere, Hellas Verona climbed to fifth with a 4-1 win at Bologna as the newly promoted side continued their impressive form.
Goals from Fabrizio Cacciatore and Juan Iturbe had given the vistiors a 2-0 lead at half-time, and although Alessandro Diamanti scored a penalty for Bologna, further strikes from Luca Toni and Jorginho sealed a fine away win.
Sampdoria remain in the bottom three after a 2-2 draw with Torino but were left fuming when the referee blew the whistle for half-time just seconds before they thought they had put some daylight between themselves and the Granata.
Delio Rossi's winless side were 1-0 up when Nicola Pozzi appeared to have doubled their advantage, but referee Andrea Gervasoni decided otherwise.
And Samp failed to hold their lead, with Ciro Immobile and Alessio Cerci putting Torino in front with second-half goals.
The Blucerchiati did manage an equaliser, though, as Eder's stoppage-time penalty helped them at least secure a point.
Meanwhile, goals from Danilo and Antonio Di Natale helped Udinese to a 2-0 win over Cagliari, while Parma beat struggling Sassuolo 3-1 at the Ennio Tardini.
The spoilts were shared between Catania and Genoa, with the game in Sicily finishing 1-1.