Inter have 59 points from 27 games after their fourth draw in five league games and maintain the four-point lead they started the weekend with over Milan, who failed to turn dominance into goals in another goalless draw in Rome on Saturday.
AS Roma are three points further back in third.
Jose Mourinho, serving the second game of his three-match touchline ban for his controversial handcuffs gesture against Sampdoria two weeks ago, fielded three strikers in his starting XI.
Nevertheless his team were sterile in attack in a listless first half, when Genoa's Giandomenico Mesto and Giuseppe Sculli and Inter's Dejan Stankovic all had crisp but central shots easily saved.
The champions made three substitutions in a bid to shake things up after the break with the struggling Samuel Eto'o among those making an entry from the bench.
The Cameroon striker had a shot from outside the box well saved by Marco Amelia and Maicon came close with a diagonal strike as Inter finally put the visitors under pressure in the closing stages.
"We had a lot of players who travelled and played 90 minutes with their national teams this week," Inter's technical director Marco Branca told Sky television. "You cannot always be at the top in terms of concentration and desire.
"It's a point and it's one game less to the end of the season. Today's match wasn't brilliant. That can happen during the course of the championship."
Mourinho is refusing to talk to the media before or after league matches during his ban.
Palermo regained fourth place earlier on Sunday when Fabrizio Miccoli's late goal gave them a 1-0 home win over relegation-threatened Livorno.
Palermo have 46 points from 27 games, two more than Juventus who won 2-1 at Fiorentina on Saturday.
Sampdoria are also in the chase for Champions League qualification after a 2-1 comeback win at home over Lazio that puts them one point behind Juve in sixth.
Stefano Guberti's piledriver and a volley by Giampaolo Pazzini clinched it in the first half after Sergio Floccari's early opener for the Rome club.
Lazio, who are just three points above the relegation zone, had Mauro Zarate sent off for dissent in the 77th minute.
