In a game which lacked clear-cut goalscoring chances, the closest either side came to breaking the deadlock was when Lazio forward Hernanes hit the post early in the second half.
Genoa improved as the game progressed, but their constant search for Luca Toni inside the Lazio penalty area proved futile as they failed to win for the third home game in a row.
Sergio Floccari's deflected shot in the second minute proved to be nothing more than a false dawn as far as the first half was concerned.
The former Genoa striker missed what was the one and only decent chance in the first half when he beat the offside trap, but failed to make the most of his opportunity as the Genoa defence recovered their ground.
Floccari then found Kakha Kaladze in his way after Cristian Ledesma dissected the Genoa defence for a second time minutes later.
Kaladze, promoted to the starting XI following the sale of Andrea Ranocchia to Inter Milan, was proving to be unbeatable for the Lazio attack and he later got in the way of Mauro Zarate's goalbound volley.
The first sign of life from the home side came just two minutes before the interval when Giandomenico Mesto and Mattia Destro combined with the latter's cross cut out by Ledesma.
And Destro was incensed when referee Andrea Romeo blew his half-time whistle just as he was lining up a shot from the edge of the penalty area.
The game came to life in the second half when Hernanes' shot from 20 yards rebounded off the inside of the post and Zarate could not turn in the rebound from a tight angle.
Stefano Mauri shot wide from an angle as Lazio moved up a gear, but Genoa responded.
Toni and Kaladze both failed to get the rub of the green as the ball bounced around inside the six-yard box following a corner and Bosko Jankovic's shot was then fumbled by Nelson Muslera to Toni, who was in an offside position
A direct free-kick from Jankovic stung Muslera's hands on the hour mark before a courageous saving header from Stephan Lichtsteiner prevented Toni from nodding Destro's cross in from six yards.
Jankovic was finally seeing more of the ball and inspiring the home side.
His delicate lob into the path of Marco Rossi provided the next opportunity, but the onrushing Muslera thwarted the Genoa captain.
Toni was Genoa's target man for the final 20 minutes, but he could not make the most of a scant service as the game ended without a goal.