Del Potro, seeded second, won 70 percent of the points on serve en route to a 6-3, 6-4 victory over Philipp Petzschner. He saved all four of the break points he saw in the first set and dropped only six points on serve in the second.
Anderson got past Marcos Baghdatis 6-2, 7-6 (7-5) behind five service breaks in 10 receiving games.
Darcis turned the match in the second set by winning three-quarters of the points. Davydenko won the first three games of the third set before Darcis came back again.
Nieminen got the only break of the match in taking the second set. There were no break points in the first set and Nieminen saved the only one Haase managed on the day.
The win puts Nieminen into the second round against No. 1-seed Jo-Wilfried Tsonga.