Hewitt was tested before disposing of Lukas Rosol 6-4, 3-6, 6-1 and Nalbandian advanced with a 6-4, 6-2 winner over Marcel Granollers.
No. 15 seed John Isner will meet Hewitt in the second round and Nalbandian's opponent will be 24th-seeded Jerzy Janowicz.
All of the seeded players in this Masters series tournament receive a bye into the second round.
Denis Istomin earned a match against No. 2 Roger Federer by getting past Vasek Pospisil 7-6 (7-5), 6-3 and Kevin Anderson will take on No. 4 David Ferrer after disposing of Victor Hanescu 7-6 (8-6), 6-3.
Notable deaths of 2014 [PHOTOS]