Roddick, who is bidding for his fifth title at Queen's Club, defeated 15th-seeded Kevin Anderson of South Africa 6-4, 6-4, while Murray overcame Janko Tipsarevic of Serbia 6-4, 7-6 (3). Adrian Mannarino upset Juan Martin del Potro 7-6 (3), 7-6 (7).
Nadal was never seriously threatened, but Stepanek proved to be a tenacious opponent.
The 32-year-old Czech saved two match points at 5-3 in the second set and won five straight games to take the match into a third set.
In the final set, Nadal broke to lead 2-0 but then had to hold off three break points to hold for 3-0 before another break all but sealed the match.
"I think I played much better than yesterday," Nadal said. "I was playing a very confident match but at 5-3, 40-15 he played well and I made a few mistakes. But the turning point of the match was the beginning of the third set, especially the first game, was tough, and after that I think I played my best."
Roddick also had to withstand some early pressure from Anderson.
In a match of big-servers, Anderson claimed two break points in Roddick's opening service game, but the American held before breaking to lead 3-2 and served out the set.
The second set followed a similar pattern, Roddick fighting off an early break point before moving ahead when Anderson netted a forehand.
"I thought it was solid," Roddick said. "I had a game plan, I stuck to it. There was never going to be a lot of breaks out there today with the way we were both serving, but that's grass-court tennis."
Murray managed a strong challenge from Tipsarevic, who won their only previous grass-court match when they played at Queen's Club five years ago.
The 14th-seeded Tipsarevic broke in the opening game, but Murray evened it at 3-3 and broke again in the 10th game when his opponent made a forehand error.
Tipsarevic again broke at the start of the second set, but Murray increased the pressure and after failing to convert two break points at 3-2, he tied it 4-4 before dominating the tiebreaker.
"I thought it was a high quality match," Murray said. "We both played very well especially at the end of the second set, a lot of good rallies and long games. It was a really good test."
Two Frenchmen retired with injuries. Michael Llodra quit because of a leg problem with fifth-seeded Jo-Wilfried Tsonga leading 4-3. In another all-French matchup, sixth-seeded Gilles Simon retired with back pain when trailing Mannarino 6-7 (4), 6-4, 3-0 in a delayed second-round match. Mannarino then upset del Potro.