American Stephens notched just her second win against a Top 10 opponent, rallying to overcome the third-seeded Russian 2-6, 7-6 (7-5), 6-3 at Lindner Family Tennis Center.
Sharapova, hampered by a left hip injury, was making her first appearance since Wimbledon.
Azarenka, meanwhile, needed a second-set tiebreaker to turn back an upset bid by American qualifier Vania King, 6-1, 7-6 (8-6) and reach Round 3.
Also registering first-round wins Tuesday were 10th-seeded Caroline Wozniacki of Denmark, who breezed past China's Peng Shuai 6-1, 6-1, and No. 14 Jelena Jankovic of Serbia, who outlasted Germany's Sabine Lisicki, 7-6 (7-5), 5-7, 6-2.
Other opening-round winners included Americans Jamie Hampton and Varvara Lepchenko, Germans Mona Barthel and qualifier Andrea Petkovic, Russian Ekaterina Makarova, Slovak Magdalena Rybarikova, lucky loser Monica Niculescu and Slovenian qualifier Polona Hercog.
2014: The Year in Music [PHOTOS]