Not sure where this would rank all time, but I was just reading about the 1915 Detroit Tigers. They won 100 games but lost the pennant to the Red Sox.
The Tigers arrived at Fenway on September 16th just 2 games back of the Sox for a huge 4 game series. They split the first two games, and then on the 18th Harry Coveleski and Ernie Shore each pitched shutout ball until the bottom of the 12th when the Sox scored on two infield hits and an error. The Sox won the next day as well when some dumb rookie pitcher named Babe Ruth beat the Tigers, effectively ending the Tigers' pennant hopes.
At the time it was considered quite a big deal.
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