This was the third time Appel, a senior, had been chosen in the baseball draft.
Appel became Stanford's all-time strikeout leader this season with 372 and ranked third in the Pacific-12 Conference with a 2.12 earned run average.
Houston had the No. 1 choice for the second straight year, having selected shortstop Carlos Correia with the top pick in 2012.
Appel was the eighth overall pick last year, chosen by the Pittsburgh Pirates. The player and the team, however, could not reach a contract agreement and Appel returned to Stanford for his senior year. He also was taken out of high school in the 15th round by the Detroit Tigers in 2009 but turned down a contract offer.
The Chicago Cubs selected San Diego third baseman Kris Bryant with the second pick and Colorado next chose Oklahoma pitcher Jonathan Gray.
The rest of the Top 10 was made up of high school pitcher Kohl Stewart (by Minnesota), high school outfielder Clint Frazier (by Cleveland), North Carolina third baseman Colin Moran (by Miami), high school pitcher Trey Ball (by Boston), Stephen F. Austin shortstop Hunter Dozier (by Kansas City), high school outfielder Austin Meadows (by Pittsburgh) and high school pitcher Phillip Bickford (by Toronto).