Italy dominated the first hour and Portugal were rescued by goalkeeper Rui Patricio who twice denied Ciro Immobile when the forward looked set to score. He also saved Lorenzo Pellegrini's header from close range in stoppage time.
Portugal have seven points from three games in the three-team group, two ahead of Italy who have finished their campaign. Poland, who visit Portugal for the group's final game on Tuesday, have one point and have already been relegated.
It was the second time in a year that Italy were eliminated from a competition by a 0-0 draw at the San Siro, having failed to qualify for this year's World Cup following the same result against Sweden last November.
Scotland's hopes of earning promotion to League B of the Nations League were boosted after a convincing 4-0 win over 10-man Albania in Shkoder on Saturday.
Serbia closed in on promotion to the Nations League second tier after a 2-1 home win over neighbours Montenegro on Saturday left them top of Group 4 in League C.
The Serbians, who won with first-half goals from Adem Ljajic and Aleksandar Mitrovic, have 11 points from five games, four more than Montenegro who can no longer clinch top spot.