[6] Graham attended Reagan High School in Houston, winning a Texas state baseball championship in 1952.

[9] In order to earn money to support his wife and two children at the time, Wayne left school to pursue a professional baseball career.

Graham was named Texas minor league player of the year in 1962 after hitting .311 for the Dallas-Fort Worth Rangers.

[9] Graham then appeared in twenty games for the 1964 New York Mets under the tutelage of legendary skipper Casey Stengel.

[14] Those five national titles in six years eventually led to Graham being named Junior College Coach of the Century by Collegiate Baseball.

[15] In his 11 seasons at San Jacinto, Graham posted a 675–113 record (.856 win percentage), earned five national coach of the year awards, and produced multiple professional players, most notably pitchers Roger Clemens and Andy Pettitte.

[14] He inherited a program that had tallied only seven winning seasons in 78 years of Southwest Conference play[14] and had only finished above fourth place once.

[14] Graham's crowning achievement was the 2003 College World Series, in which Rice won its first national championship in any sport in its 91-year history.

[14] Graham's Rice teams produced first-round picks Jose Cruz, Jr. (1995), Matt Anderson (1997),[14] Lance Berkman (1997),[14] Bubba Crosby (1998), Kenny Baugh (2001), Jon Skaggs (2001), David Aardsma (2003), Philip Humber (2004),[14] Jeff Niemann (2004),[14] Wade Townsend (2004, 2005),[14] Joe Savery (2007), and Anthony Rendon (2011).

Rice won four consecutive games and rallied late in the championship to upset #11 nationally ranked Southern Miss 5–4 on a walk-off double.