It's a rare occurrence that Major League Baseball hasn't seen happen since 1990, when the Red Sox and Reds each started 3-0 before the Yankees and Indians started their respective seasons. The Reds went on to win the World Series that season, making them the third team on this list of rare squads to win the Fall Classic after getting a head start on the competition. The other two such teams were the 1927 Yankees and the 1918 Red Sox.
In 1927, the Yankees were one of three teams, along with the Washington Senators and Pittsburgh Pirates, to start 3-0 before the New York Giants or Boston Braves had played a single game. The Yankees not only won the World Series that season, but they knocked off their fellow quick-starting Pirates in the Fall Classic to do so.
Nine years earlier, the Red Sox raced out to a 3-0 start, all while the Indians and Tigers were waiting to start their seasons. Boston went on to win the World Series, the last time they would do that until 2004.
Even factoring in those cases, in no instance dating back to 1900, has a team been in the Dodgers' position of having a chance to finish the day 3-0 while the majority of the league awaits its Opening Day. Los Angeles won both games against Arizona in Opening Series 2014 in Australia last weekend and will take part in tonight's Opening Night game against the Padres.
In every other instance of a team starting 3-0 before other teams had started their season, only a handful of teams were still waiting to start their season by the time a team was 3-0. Some of those situations also occurred during the early 1900s, when the National League used to start its season up to a week earlier than the American League.
NL teams had their Opening Day on April 17 in 1902, for example, while the majority of AL clubs didn't start play until April 23. The Cubs started 4-0 before six teams (Philadelphia Athletics, Chicago White Stockings, Cleveland Broncos, Detroit Tigers, St. Louis Browns and Washington Senators) opened their seasons. The following year, the NL opened its season on April 16 and the AL didn't start play until April 20, allowing the Pirates to begin the season 4-0 before any of the eight AL teams had played a single game.
Three years later, the Boston Beaneaters also started 4-0 before four teams -- the White Sox, Tigers, Cleveland Naps and St. Louis Browns -- had started their seasons. Boston began play on April 12, while that quartet of clubs did not start until April 17.
The only other teams to start 3-0 before at least one other team had played a single game are the Brooklyn Robins (1919), Yankees (1933), Pirates (1933), Boston Bees (1939), Tigers (1966), Minnesota Twins (1966) and Atlanta Braves (1982).