Jones was known for being a first-round draft pick (3rd overall in 1982) by the Padres out of Thomas Jefferson High School in Dallas, Texas. While in high school Jones had gained national attention for striking out 28 batters in a 16-inning play-off game while throwing 251 pitches. Jones claimed in a 2004 interview that his arm was so sore two days after the marathon effort that he could not throw a baseball from third base to first base.
Jones threw a one-hit shutout against the first-place Houston Astros in his big league debut on September 21, 1986. He was the first pitcher to throw a one-hitter in his debut game since Billy Rohr in 1967. He is currently the pitching coach for the Peoria Padres of the Arizona League.