Davis has won seven singles titles on the ITF tour in her career. On July 7, 2014, she reached her best singles ranking of world number 44. On May 26, 2014, she peaked at world number 295 in the doubles rankings.
After a third round appearance in a Grade 1 tournament in Carson, California, she won her first junior tournament at a Grade 3 tournament in Philadelphia, Pennsylvania, defeating Brooke Bolender in three sets. She finished 2009 with a quarterfinal appearance at the US Open, before a third round loss at the Dunlop Orange Bowl.
Davis reached one quarterfinal in the first four months, before reaching the final of the Easter Bowl, losing to Krista Hardebeck. She again lost in the final of the tournament, this time the 51st Trofeo Bonfiglio to Beatrice Capra. In November 2010, she went on an 18-match winning streak, winning the Grade 1 tournaments, Yucatán World Cup and the Eddie Herr youth tournament, as well as the Grade A Orange Bowl tournament. She finished the year a career high world number three on the junior tour.
Davis made it through the qualifying rounds to get her into the main draw of the 2012 French Open, where she won her first main draw Grand Slam match against 30th seed Mona Barthel in straight sets. In the second round, she lost to compatriot Christina McHale in straight sets.
At the Australian Open, Davis beat Julia Görges to advance to the third round of a Grand Slam tournament for the first time. There, she was defeated by Eugenie Bouchard. At the BNP Paribas Open, Davis defeated world number 4 Victoria Azarenka in the second round, marking her first victory over a top-10 player and a Grand Slam champion. She then defeated Varvara Lepchenko, but withdrew in the fourth round due to illness. At the Sony Open in Miami, she won her first-round match with Zhang Shuai, and lost in the second round to Ana Ivanovic. Following an early exit at the French Open, she advanced to the quarterfinals of the Aegon International, losing to Madison Keys.
Davis is noted for her powerful backhand, as well as for her footwork around the baseline. Her tendency is to play aggressively and go for winners. She is rather short in stature for a tennis pro, which she compensates for with power generated from her legs and core. She prefers playing on clay and hard courts.