The most famous play by a Major Leaguer was by BYU's Danny Ainge. Ainge dribbled the length of court and shot a buzzer beater to defeat Notre Dame in 1981. Ainge played parts of three seasons as an infielder for the Toronto Blue Jays before winning NBA championships with the Boston Celtics.
Longtime OF Kenny Lofton was a backup point guard for the University of Arizona during their Final Four run in 1988. The Arizona team also included future NBAers Sean Elliott and Steve Kerr. Lofton is one of only two players who played in a Final Four and a World Series.
The other was pitcher Tim Stoddard. As a member of North Carolina St team in 1974, the Wolfpack won the NCAA championship that included future basketball Hall of Famer David Thompson. He went on to be a part of two Baltimore Oriole Word Series teams(1979 and 1983-winning it all in '83). Stoddard is the only player to win championships in both.
Other MLB players who played in the "big dance" include:
-Dave DeBusschere (1962-63- White Sox pitcher) played for University of Detroit and became a NBA Hall of Famer with the New York Knicks
-Dave Winfield became a Hall of Famer in a baseball and starred for University of Minnesota's 1972 Big Ten
-Mark Hendrickson(2002-2011) played college ball at Washington St
-Cotton Nash(1967, 1969-70) played for Kentucky and later in NBA and ABA
-Ron Reed(1966-1984) played his college ball at Notre Dame and won a World Series with the Philadelpha Phillies in 1980
When you watch the NCAA tourney, you will undoubtedly watch some future NBA stars, but you may catch a future big league baseball player also.