Well this isn't the all time answer, but i know for a fact the Yankees just held the Red Sox to a Red Sox team record 31 scoreless in their sweeping of the Red Sox tonight
Oroieols
The Major League Baseball team with the most consecutive scoreless innings is 56 by the Pittsburgh Pirates. They have held that record since 1903.
i believe its 59 by Orel Hershiser, however, it would have been 67 had the postseason counted
In 1966, the Baltimore Orioles did not give up one single run -- earned or unearned -- to the L.A. Dodgers in the last 33 innings of the Series.
I think35 innengs
Babe Ruth with 29 2/3 consecutive scoreless innings pitched in World Series play.
549873938737 innings
In 1903 the Pittsburg Pirates were held scoreless for 52 innings.
36
NL - 56 - Pittsburgh, June 1 to June 9, 1903. AL - 54 - Baltimore, September 1 to September 7, 1974.
Cy young
16