Stepanek ousted seventh-seeded Mikhail Youzhny 6-4, 5-7, 6-4. Stepanek ended up with five breaks, with three coming in the third set.
Monfils was on the court less than an hour in dispatching No. 8-seeded Jurgen Melzer 6-3, 6-3. Monfils had 15 aces and was good on more than 70 percent of his first serves. He dropped 11 points on serve.
Sixth-seeded Florian Mayer barely escaped an upset, getting past Lukasz Kubot 7-6 (7-2), 4-6, 7-5. He fought off four break points in the third set before getting the late break that allowed him to reach the second round.
But No. 5-seeded Alexandr Dolgopolov rolled over Sergiy Stakhovsky 6-4, 6-2. He didn't lose his serve despite landing just 44 percent of his first serves.
Also Tuesday, Grega Zemlja beat John Millman 6-2, 6-2; qualifier Evgeny Korolev edged past Marcos Baghdatis 7-5, 7-6 (7-3); Viktor Troicki defeated Matthias Bachinger 6-3, 6-2; and Ernests Gulbis eliminated Jarkko Nieminen 6-4, 6-2.
Notable deaths of 2014 [PHOTOS]