The result was the first time the derby, in a league fixture, had ended goalless since 1989 and ended Milan's run of four straight wins in the clash.
Juventus have a five-point advantage over Milan and early season surprise packages Lecce, while Inter, unbeaten but with five draws from seven games, are eight points behind the leaders.
While there were no goals to entertain capacity crowd of nearly 80,000 at the San Siro, both sides created opportunities and the game produced great entertainment.
In the end, though, the two prolific strikers on show, Inter's powerful Brazilian Adriano and Milan's Ukrainian Andriy Shevchenko, were mastered by their markers and suffered from a lack of incisive service.
Inter's best chances fell early in the match, with Christian Vieri shooting straight at Dida in the third minute and firing wide from a good position.
Vieri had scored in his previous two games, including Wednesday's 5-1 Champions League win at Valencia, but coach Roberto Mancini said that despite the missed chances the striker was getting back to form.
"It was a shame those chances didn't go in but to be frank he played better tonight then in the last two games including Valencia," he said.
KEPT QUIET
Despite the absence through injury of Milan's Dutch defender Jaap Stam, Adriano was largely kept quiet by Alessandro Nesta, although on the stroke of halftime he produced a brilliant piece of skill to make space for a shot but fired wide from a tight angle.
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Inter's best effort after the break came from an Adriano header which Dida parried and Nesta did well to clear ahead of the waiting Inter striker.
Milan were at their most dangerous when attacking down the flanks but three times they failed to convert good crosses with Andriy Shevchenko, Kaka and Massimo Ambrosini failing to test Inter keeper Alberto Fontana.
The defences of both teams have been criticised this season and Mancini was pleased with the clean sheet.
"It was a test that we passed," said Mancini, "We showed that against a team of Milan's calibre we can go 90 minutes without conceding a goal.
"I am satisfied with the way we played. It was a good performance against a great side. We had our chances but a draw was fair and I can cope with a point against Milan," he added.
Milan coach Carlo Ancelotti was also happy enough.
"I'm satisfied with the way that we played. We were very competitive and played some good football. A draw was fair enough and the defence did very well to keep them out," he said.
