Angelique Kerber overcame a stomach bug to defeat the ninth-seeded Lisicki 4-6, 6-4, 6-1 in an all-German match, and Simona Halep of Romania downed the 15th-seeded Hantuchova of Slovakia 3-6, 6-2, 7-6 (4) after 2 hours, 32 minutes.
Kerber, a U.S. Open semifinalist who won her first WTA title at the Open GDF Suez last week, will play Tsvetana Pironkova of Bulgaria.
"I hung in there despite stomach problems," Kerber said. "I think we both played a great game. It was a difficult match for me because she's not just a great player but a great friend. We have played on the Fed Cup together, so to beat her wasn't easy."
Lisicki disagreed with Kerber about her own form.
"I think in general I played an awful match," Lisicki said. "I think in the last 10 tournaments I didn't make as many unforced errors as I did today alone."
Playing predominantly from the baseline on center court at the Khalifa Tennis Complex, Halep's serve in the third-set tiebreaker proved instrumental in knocking out last week's Pattaya Open champion.
"I stayed calm and relaxed in the third set. Basically I tried to put the ball onto the court," Halep said. "I fought really well against a great player. It was a very difficult match for me because I had pain in my leg. It was important for me to win today for my confidence."
Julia Goerges of Germany, seeded 16th, downed Anastasia Yakimova of Belarus 6-2, 6-2 and Lucie Safarova defeated Urszula Radwanska of Poland 6-3, 6-4. The Czech will play fourth-ranked Caroline Wozniacki on Wednesday.
Petra Cetkovska of the Czech Republic beat Petra Martic of Croatia 7-6, 7-5, Anabel Medina Garrigues topped Klara Zakopalova of the Czech Republic 6-4, 6-1, and Romania's Sorana Cirstea won 6-4, 6-1 against Jarmila Gajdosova of Australia.