The first Yankee Stadium was built in 1923. The Yankees won the World Series (for the first time) over the New York Giants that year.
The first year of the 'overhauled' Yankee Stadium was 1976. The Yanks won the pennant (for the first time in 12 years), but lost the World Series to the Big Red Machine.
The first year of the new Yankee Stadium was 2009. The Yankees defeated the Philadelphia Phillies to win their 27th title (for the first time in nine years).
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(The '09 Yanks also became the third team to win the clinching game of the World Series in their new ballpark, joining the 1912 Red Sox and 2006 Cardinals.)