Azarenka was broken early by Swiss Romina Oprandi to go 2-0 behind but responded with three breaks to take the opening set.
She raced 3-0 up in the second stanza before sealing the match 6-2 6-3 as the six-foot Belarusian's first serve dominated.
However she had to save six of seven break points won by her 5'6" opponent.
Defending champion Azarenka is now 10-0 in 2013 having won the Australian Open. She will retain the number one spot in the WTA rankings if she reaches the final and Serena Williams fails to reach the semis.
She withdrew from her Brisbane International semi-final against Williams at the start of the year with a toe infection.
Oprandi won their first meeting on clay in 2007 while Azarenka won the two others, both last year, on the grass of Wimbledon and hardcourt of the China Open quarter-finals.
Azarenka will next play American Christina McHale who knocked out Lucie Safarova.
American teenager Stephens, who beat Williams in the Melbourne quarter-finals, was ousted by Czech Klara Zakopalova after two close tie-breaks.
The 16th-ranked Stephens won the first set but ultimately went down 4-6 7-6(5) 7-6(5).
The other seeds to drop out on Wednesday were ninth seed Marion Bartoli, who has been suffering with flu and went down 6-4 6-4 to Svetlana Kuznetsova, and Italian 15th seed Roberta Vinci, who lost 6-2 5-7 6-0 to Pole Urszula Radwanska.
The latter's sister, fourth seed Agnieszka Radwanska, moved safely through to the third round with a 6-3 6-2 defeat of Australia's Anastasia Rodionova while former world number one Caroline Wozniacki faced some stiff resistance initially from Sorana Cirstea before winning 7-6 6-0.
ATP Doha round two results
Svetlana Kuznetsova (Russia) beat 9-Marion Bartoli (France) 6-4 6-4
8-Samantha Stosur (Australia) beat Monica Niculescu (Romania) 6-4 1-6 6-3
10-Caroline Wozniacki (Denmark) beat Sorana Cirstea (Romania) 7-6(7) 6-0
Daniela Hantuchova (Slovakia) beat Ekaterina Bychkova (Russia) 6-3 1-6 6-3
Urszula Radwanska (Poland) beat 15-Roberta Vinci (Italy) 6-2 5-7 6-0
7-Petra Kvitova (Czech Republic) beat Ekaterina Makarova (Russia) 6-4 0-0 (Makarova retired)
1-Victoria Azarenka (Belarus) beat Romina Oprandi (Switzerland) 6-2 6-3
Klara Zakopalova (Czech Republic) beat 16-Sloane Stephens (U.S.) 4-6 7-6(5) 7-6(5)
11-Nadia Petrova (Russia) beat Hsieh Su-Wei (Taiwan) 3-6 6-2 6-4
13-Ana Ivanovic (Serbia) beat Simona Halep (Romania) 6-3 0-0 (Halep retired)
Christina Mchale (U.S.) beat 17-Lucie Safarova (Czech Republic) 6-4 6-2
4-Agnieszka Radwanska (Poland) beat Anastasia Rodionova (Australia) 6-3 6-2
6-Sara Errani (Italy) beat Timea Babos (Hungary) 6-4 6-0