Lasicki moved on, but four other seeded players were eliminated in upsets. After all eight seeds survived the first round, second-seeded Peng Shuai of China, fifth-seeded Julia Goerges of Germany, sixth seeded Roberta Vinci of Italy, and eighth seeded Monica Niculescu of Romania were knocked out by unseeded opponents in the second round on Wednesday.
The 15th-ranked Lisicki had highs and lows in her second-round match against Barthel, hitting 27 forehand winners and 11 backhand winners, but mixing in six double faults and 66 unforced errors.
Lisicki's match was delayed by rain, and her timing was disrupted by a swirling breeze on center court. She pushed through in her first tournament of the season, and overcame the frustration of losing the second set to win the third in 35 minutes.
Lisicki's quarterfinal opponent will be against fellow German Angelique Kerber, who beat the ailing Goerges 6-2, 6-3.
The 67th-ranked Barthel stretched Lisicki at times with her heavy serve and strong groundstrokes. Lisicki made adjustments after the second set, and improved on her court coverage and footwork after being urged on by her coach.
She served for the match at 5-2, but lost three straight points and eventually the game. However, Lisicki then broke Barthel's serve for the third time in the set.
"It's great to have a challenge like that," Lisicki said. "That's why we play tennis.
"Mona gave me a great match, and it's good to have that challenge early in the year."
The 52nd-ranked Lucie Hradecka, a French Open doubles champion and member of the Czech Republic's Fed Cup-winning team, overpowered 17th-ranked Shuai 6-4, 6-3 in 73 minutes.
Hradecka's power prevented Shuai from settling into any rhythm, and the Chinese player, now bound from Melbourne and the Australian Open, never looked at ease.
"My serve was working well," Hradecka said. "I'm just so happy with this win, and for the moment I can't believe I did it."
Vinci was beaten 6-3, 6-4 by Elena Vesnina of Russia. Niculescu lost 6-0, 6-2 to China's Zheng Jie.
Third-seeded Svetlana Kuznetsova, the former world No.2, was scheduled to play later Wednesday.