Nine of the 10 leading women's tennis players -- all but No. 10 Marion Bartoli -- were in the field when the Olympics started. However, world No. 2 Agnieszka Radwanska and fifth-ranked Samantha Stosur were beaten in first-round matches.
Azarenka is No. 1 for a 23rd week. With Radwanska's loss, only third-ranked Maria Sharapova can catch Azarenka for the top spot after the Olympics but she has to win the gold medal and have Azarenka lose her second-round match.
Azarenka has 8,800 ranking points and Radwanska totals 8,530 with Sharapova in third at 8,370.
Serena Williams, already through the Olympics third round, is fourth with 7,360 points and Stosur is fifth with 6,195.
Petra Kvitova (5,275) is No. 6, ahead of Angelique Kerber (5,170) and Caroline Wozniacki (4,091). Sara Errani is ninth with 3,620 and Bartoli has 3,400 points.
Bojana Jovanovski won the Baku Cup -- the only non-Olympic WTA event on the schedule last week -- and goes from 97th to 68th in the world rankings. Julia Cohen, who lost in the Baku finals, improves from 134th to a career high of No. 97.