The Belarussian, Australian Open champion the last two years, raced to a 5-0 lead and was 5-1 up when the match was interrupted by rain on Court Suzanne Lenglen.
Beck benefited from a series of unforced errors from Azarenka to reduce the gap and led 30-0 on her opponent's serve at 5-4 when the world number three regained composure and clinched the opening set after 69 minutes.
The second set was straightforward as Azarenka booked a third-round meeting with French 31st seed Alize Cornet.
Former world number one Jelena Jankovic moved into the third round of the French Open with a win over Garbine Muguruza.
It is easy to forget Jankovic ended 2008 as the top player in the world, with a first Grand Slam title seemingly not far away.
But things did not quite go to plan for the Serb, now aged 28 - and arriving at this year's French Open seeded 18 she is not on many people's lists of potential champions.
There have been signs this year though that Jankovic is returning to the kind of form that once made her a fixture in the top 10 and regular title winner.
On Thursday at Roland Garros she moved through with an impressive 6-3 6-0 victory over Spain's Muguruza, storming through the last 12 games after losing the first three and getting off court just as the rain began to fell.
In the first round against former world number five Daniela Hantuchova she recovered a 5-0 second-set deficit so there is clearly nothing wrong with her fighting spirit.
"Since Miami this year I've felt the confidence coming back and I feel like I'm competing as a top player again," Jankovic told Reuters.
"I know that when I'm healthy and free of injuries I'm still capable of playing great tennis.
"I started slowly today but then won 12 games in a row. I just beat the rain too, so that's a relief."
From the US Open in 2006 when Jankovic reached her first Grand Slam semi-final she enjoyed a run of consistency that took her all the way to number one in the world, reaching three semi-finals and a final in the next eight Grand Slam tournaments.
Since losing to Serena Williams in the 2008 US Open final she has found it much harder to make an impression at the majors with her 2010 run to the semi-finals at Roland Garros when she lost to Samantha Stosur her best effort in the past four years.
Jankovic ended last year out of the top 20 for the first time since 2005 and appeared to be on the decline as injuries to her back and thigh caught up with her.
But she is not finished yet.
"I'm only 28," she joked, when it was suggested she was one of the Tour's more mature players.
"We are seeing now that players are sticking around much longer and still challenging for titles into their late 20s and into their 30s, just look at Serena.
"(Francesca) Schiavone also won the French when she was 30 I think recently so just because you're late 20s doesn't mean that it's time to start dropping down the rankings.
"I feel more mature now, I know my game more. When I was younger I didn't have so many niggling injuries but the good side now is that I'm a more complete player.
"When I reached the semi-finals at Miami this year it was a real lift and I also won my 13th title in Bogota, so it's been an upward curve this season and I'm enjoying it and am motivated."
China's only grand slam singles champion Li Na was bundled out of the French Open by American Bethanie Mattek-Sands, losing a rain-interrupted match 5-7 6-3 6-2.
Sixth seed Li, who became a flag-bearer for Asian tennis in 2011 when she won the French Open, edged the first set but after two lengthy rain breaks her game fell apart.
Mattek-Sands, wearing knee-high black socks, resumed after the second interruption 4-3 ahead in the second set and then reeled off seven games in a row.
Li eventually stopped the rot to break serve as Mattek-Sands served for the match at 5-0 and then held her own to reduce the deficit but her revival came too late.
With rain still falling and play stopped on many other courts the 66th-ranked American held her nerve and sealed victory when her opponent netted a forehand.
Li refused to make excuses for her defeat.
"I know for sure that I don't normally lose seven games in a row," she told reporters. "It was very tough conditions, coming back to the court three times.
"But for both players it was the same.
"I should find out what happened and I'll talk to myself, my team to see what happened."
3-Victoria Azarenka (Belarus) beat Annika Beck (Germany) 6-4 6-3
Bethanie Mattek-Sands (U.S.) beat 6-Li Na (China) 5-7 6-3 6-2
7-Petra Kvitova (Czech Republic) beat Peng Shuai (China) 6-4 6-3
9-Samantha Stosur (Australia) beat Kristina Mladenovic (France) 6-4 6-3
Marina Erakovic (New Zealand) beat 16-Dominika Cibulkova (Slovakia) 6-2 2-6 6-4
17-Sloane Stephens (U.S.) beat Vania King (U.S.) 6-1 6-3
18-Jelena Jankovic (Serbia) beat Garbine Muguruza Blanco (Spain) 6-3 6-0
Paula Ormaechea (Argentina) beat 27-Yaroslava Shvedova (Kazakhstan) 6-4 7-6(6)
31-Alize Cornet (France) beat Silvia Soler Espinosa (Spain) 6-1 6-3
Jamie Hampton (U.S.) beat Anna Karolina Schmiedlova (Slovakia) 7-5 6-2
Zheng Jie (China) beat Melanie Oudin (U.S.) 6-3 6-1