Both squads remained winless this season and time could be running out for Inter coach Gian Piero Gasperini and Roma's Luis Enrique.
Inter lost its three previous matches this season, capped by an embarrassing 1-0 home defeat to Turkish debutante Trabzonspor in the Champions League earlier this week.
Inter was beaten 2-1 by AC Milan in the Italian Super Cup last month and lost 4-3 at Palermo in its Serie A opener last weekend, allowing four goals in a league match for the first time in more than seven years.
Roma is also in crisis, having opened the Italian league with a 2-1 home defeat to Cagliari after also losing a Europa League playoff to Slovan Bratislava.
Both sides produced numerous chances at the San Siro, but both squads also appeared disorganized at times.
Roma got more bad news when goalkeeper Maarten Stekelenburg had to be carried off on a stretcher after getting kicked in the head during the first half, although medical tests reportedly showed no major injuries.
Earlier, Cagliari took the early lead in Serie A with a 2-1 win over newly promoted Novara.
On Sunday defending champion AC Milan visits Napoli and Juventus hopes to continue its strong start at Siena.
Also Sunday, it's: Atalanta vs. Palermo; Bologna vs.
Lecce; Catania vs. Cesena; Lazio vs. Genoa; Parma vs.
Chievo Verona; and Udinese vs. Fiorentina.
Under a light rain in Milan, Gasperini reverted to his preferred three-man defense and lined up Diego Forlan and Diego Milito at forward in a 3-5-2 formation.
Roma responded with a 4-3-3 spearheaded by Daniel Osvaldo, captain Francesco Totti and 20-year-old Fabio Borini.
Roma had the first chance when Osvaldo was denied from a sharp angle by Inter goalkeeper Julio Cesar in the 11th.
In the 15th, Stekelenburg charged forward to punch away a ball that Inter defender Lucio was chasing. Lucio then failed to jump over the keeper and hit the right side of Stekelenburg's head with his foot, earning a yellow card for the Brazil defender.
Stekelenburg sat up after the incident but then immediately appeared to lose consciousness, and his head dropped back to the ground. He regained his senses in the changing room before being taken to the San Carlo hospital, according to the ANSA news agency.
Italy's Sky TV reported that medical tests revealed no major injuries.
Borini put a powerful shot on goal in the 19th, drawing another save from Julio Cesar, and Inter then responded with a chance from Milito that was stopped by Roma's substitute keeper Bogdan Lobont.
In the 36th, Inter's Japan fullback Yuto Nagatomo shot wide from an angle, and Julio Cesar did well to shut down an effort from Osvaldo in the 46th.
In the 50th, Inter playmaker Wesley Sneijder placed a perfect free kick across Roma's area but Milito headed it wide.
Gasperini replaced Milito with fellow Argentine Mauro Zarate in the 58th and the forward evaded two defenders before launching a powerful shot wide six minutes later.
Zarate provided a spark for Inter and set up Sneijder in the center of the area in the 86th but the Netherlands international had his shot cleared off the line by Roma defender Simon Kjaer.
In Sardinia, Brazilian forward Thiago Ribeiro gave Cagliari the lead with a header in the 38th and Argentine forward Joaquin Larrivey doubled the lead in the 86th with a deflection off a shot from captain Daniele Conti.
Japan forward Takayuki Morimoto pulled one back for Novara in the 88th with a lob from outside the area.
Novara, which is back in the top division for the first time in 55 years, has one point.
Many Cagliari fans heeded a call from club president Massimo Cellino and wore purple to ward off bad luck, since the match was played on the 17th day of the month and 17 is considered an unlucky number in Italy.
The purple may have worked, as Cagliari has a full six points.
"It's a great starting point," said Cagliari midfielder Davide Biondini.