Robredo beat Rainer Schuettler of Germany 6-1, 6-4, and Wawrinka defeated Viktor Troicki of Serbia 6-2, 6-3.
Schuettler, the 2004 runner-up, won only 16 points in the first set and lost his serve five times.
Robredo next plays either Juan Monaco or Jeremy Chardy, while Wawrinka will face Igor Andreev or Martin Vassallo Arguello.
Philipp Kohlschreiber of Germany and Simone Bolelli of Italy also won. Kohlschreiber beat Ernests Gulbis of Latvia 6-1, 6-3 to set up a second-round match against seventh-seeded Fernando Verdasco of Spain.
"It's a very good start for the clay court season,'' Kohlschreiber said. "Overall I have to say I did everything right. I played a good match today.''
Bolelli needed more than two hours to defeat big-serving Robin Soderling of Sweden 6-4, 1-6, 6-3.
Bolelli broke Soderling in the fourth game of the third set and then held for a 4-1 lead. He clinched the match with an ace on his second match point and next faces either ninth-seeded Gael Monfils of France or Janko Tipsarevic of Serbia.
Top-ranked Rafael Nadal will begin his pursuit of a fifth consecutive Monte Carlo title in the second round against either Igor Kunitsyn of Russia or Juan Ignacio Chela of Argentina.
The Spaniard has won the French Open and Monte Carlo every year since 2005 - beating second-ranked Roger Federer in the last three finals at both events.
Nine of the top 10 players in the world are taking part this year, with only sixth-ranked Andy Roddick absent.
Federer accepted a last-minute wild card invitation Thursday. The 13-time Grand Slam champion married longtime girlfriend Mirka Vavrinec in a small ceremony in his hometown of Basel on Saturday.
Sounders FC try to get healthy before Chivas match
Robredo and Wawrinka advance at Monte Carlo
