Barthel won nine of 10 games in one stretch of a 6-1, 6-2 romp over Kerber in 61 minutes.
Kerber opened the match with a break but Barthel broke back and then ran off five more games in taking the first set. Kerber won the first game of the second set before Barthel won three consecutive games for the lead. Kerber held serve once more but Kerber took the last three games to advance.
Second-seeded Serena Williams and No. 3 Maria Sharapova had solid second-round wins Tuesday. Williams needed just 54 minutes to dispatch Daria Gavrilova 6-2, 6-1. Williams did see five break points -- saving them all -- but still won 73 percent of the points on serve.
Sharapova had five breaks in a 6-3, 6-2 win over Carolina Garcia. Sharapova took 68 percent of the points on serve and 58 percent overall in the match.
Ninth-seeded Marion Bartoli took a tight 7-6 (7-5), 6-3 decision from Francesca Schiavone while 11th-seeded Nadia Petrova, No. 15 Roberta Vinci, 16th-seeded Sloane Stephens and No. 17 Lucie Safarova all also won in straight sets in first-round matches.