On July 1, 1903, the Giants pulled off a quadruple play against the visiting St. Louis Cardinals in front of 3,685 fans at the Polo Grounds in New York. The Cardinals had loaded the bases during the sixth inning, which set up the historic play. The centerfielder for the Cardinals, Homer Smoot came to the dish hoping to plate some runs. Smoot connected on a fly ball to center, that looked like it was going to fall in, as the runners took off. The Giants centerfielder caught the ball retiring Smoot, before he fired it home to his catcher John Warner who retired St. Louis' pitcher Clarence Currie at the dish. Warner then fired to shortstop George Davis who nailed Patsy Donovan for the third out, as Donovan was trying to advance from first to second. While the third out had been recorded, neither team seemed to realize it, and St. Louis' second basemen John Farrell , who was standing at second when it all began turned the corner at third, and headed home. Warner tagged him as he tried to cross the dish for the "fourth out" of the inning.
The Giants went onto win the contest by the score of 5-2, which was due in large part to the triple play that came with a bonus out. The newspaper article that I found did not go into great detail about the four out play. However, I did confirm this fact to be true through the Society of American Baseball Research. The source they used was the New York Times. Unfortunately, I do not have access to their archives. While the article I did find does not lay out the complete story, I do consider it quite the find. Especially since it comes from the turn of the century.
The SABR source can be found here: http://tripleplays.sabr.org/tp_1900.htm