Anderson, the No. 9 seed, defeated James Ward 4-6, 6-3, 6-4, losing his serve once in the match. There was one break in each set with Anderson getting one each in the second and third sets to advance.
No. 10-seeded David Nalbandian had one of the later wins in the 24-match schedule Tuesday, taking out Vasek Pospisil 4-6, 6-2, 6-2 with two breaks in each of the last two sets.
Marcos Baghdatis, the No. 11 seed, also needed three sets before getting past Frederico Gil 7-6 (7-2), 4-6, 6-2 while 12th-seeded Denis Istomin beat Kenny De Schepper 6-4, 7-6 (7-4) and No. 13 Alex Bogomolov Jr. eliminated Martin Klizan 6-2, 7-6 (7-5).
Tuesday's other three seeds has easier times with No. 14-seeded Gilles Muller in a 6-2, 6-1 romp over Liam Broady; No. 15 Go Soeda beating Bjorn Phau 6-2, 6-2; and 16th-seeded Ivo Karlovic rolling past Lleyton Hewitt 6-3, 6-2. Karlovic's match took 64 minutes; the others, less than an hour each.
One match wasn't completed Tuesday. Paolo Lorenzi had pulled even with Tatsuma Ito 6-7 (6-8), 6-4 before play was called because of darkness.
Other winners Tuesday included Nicolas Mahut, Grigor Dimitrov, Sergiy Stakhovsky, Steve Darcis, Simone Bolelli and Xavier Malisse. Ruben Bemelmans, Edouard Roger-Vasselin, Matthew Ebden, Lukas Rosol, Lu Yen-Hsun, Ryan Sweeting, Sam Querrey, Ivan Dodig and Jamie Baker and advanced.
Notable deaths of 2014 [PHOTOS]