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Prior to playing professionally, Sanabia attended Castle Park High School in Chula Vista, California. He was drafted by the Marlins in the 32nd round of the 2006 amateur draft and began his professional career that season, playing for the GCL Marlins. With them, he went 3-1 with a 3.24 ERA in 11 relief appearances. He pitched for the Jamestown Jammers in 2007, going 2-6 with a 5.13 ERA in 15 starts. In 2008 with the Greensboro Grasshoppers, he went 5-5 with a 4.93 ERA in 19 starts. With the Jupiter Hammerheads in 2009, Sanabia went 9-5 with a 3.45 ERA in 19 games (18 starts). He began the 2010 season with the Jacksonville Suns, going 5-1 with a 2.03 ERA in 14 starts prior to his call up.
He made his major league debut on June 24, 2010, pitching 3.1 innings in relief and posting an ERA of 5.40 against the Baltimore Orioles.