Current oldest is now Billy Werber, 99, an infielder who played for the Yankees, Red Sox, Athletics, Reds, and Giants from 1930, 1933 to 1942. He is also the last surviving teammate of Babe Ruth. And he was the first ever player to have an at bat televised.
It's a very telling statement that these sorts of things are usually phrased in terms of Babe Ruth (think anyone will be saying in 80 years that "he is the last major leaguer to pitch to Barry Bonds"?). I wonder how many people are left who played against Ruth in a major league game?