The Suns selected Davis with the fifth pick of the 1977 NBA draft. He made an immediate impact, playing in 81 games and averaging 24.2 points per game in his first season, which would also be his career-high. He won the 1978 Rookie of the Year Award, and earned second teamAll-NBA honors. Over his first ten seasons, Davis averaged over 20 points per game six times, and earned trips to six All-Star Games. On February 25, 1983, Davis set an all-time NBA record when he successfully scored his first 34 points before finally missing a shot. He made his first 15 field goals and converted four straight free throws before missing a jumper with 55 seconds left in the game. Larry Costello formerly held the record, having made all of his attempts on his first 32 points for Syracuse in 1961. Over his career, Davis averaged 18.9 points, 3.8 assists and 3.0 rebounds per game. Davis was affectionately known as "The Greyhound" for his speedy style and sleek physical appearance. Suns broadcaster Al McCoy created many alternate nicknames for him, including "The Candyman", and "The Man with the Velvet Touch." Davis is the Suns' all-time leading scorer with 15,666 points. Davis's later years with the Suns were marred by recurring back problems and an ugly drug scandal. In 1987, he was called on to testify on illegal drug use by other Suns players in exchange for immunity from prosecution. Davis's decline mirrored the short decline of the Suns franchise, and at the expiration of his contract in 1988 at age 33, the team did not seriously attempt to re-sign him, offering a 1-year contract at half his previous salary. Davis signed a two-year, $1.35 million deal with the Denver Nuggets as an unrestricted free agent. He ended up playing for two years beyond this contract, and was included in a three-team trade in early 1991 that sent him to the Portland Trail Blazers for half a season. Davis finished 479 points shy of 20,000 points in a career. In the summer of 1991, he returned to Denver to close out his playing career.
Davis later served as a broadcaster for the Nuggets, and has served as a scout for the Washington Wizards. As time passed, Davis and the Suns repaired their relationship. In 1994, his No. 6 was retired by the Suns, and in 2004 he was enshrined in the team's Ring of Honor. He is the uncle of UNC assistant coach Hubert Davis, who also played for UNC and in the NBA.