Fifth-seeded Robredo won 7-6 (3), 6-3 in 80 minutes at the clay-court tournament.
Rain had interrupted earlier matches and forced a delayed start to Robredo’s tournament opener but it did not affect the two-time champion, who hit seven aces in his victory.
Robredo will face Kazakhstan’s Andrey Golubev in the next round, after he comfortably beat Maximo Gonzalez of Argentina 6-3, 6-2.
Uruguay’s Pablo Cuevas, ranked 64th, also advanced by beating sixth-seeded Paul-Henri Mathieu of France 7-6 (2), 7-6 (3) on center court.
Seventh seeded Denis Istomin of Uzbekistan was beaten in a 2 1/2 hour match by Croatia’s Franco Skugor 7-6 (5), 7-6 (7). Skugor, who is ranked 309 places below Istomin, made it through singles qualifying to play in the first round.
France’s Stephane Robert earned himself a second-round match against second-seeded Fernando Verdasco after defeating compatriot Jonathan Dasnieres De Veig 6-4, 6-1.
Also into the second round are Jarkko Nieminen of Finland, Andreas Seppi of Italy and Sweden’s Ervin Eleskovic.
Center court is sure to be packed on Wednesday evening when top-seeded Robin Soderling begins his title defense against fellow-Swede Andreas Vinciguerra.
In Stuttgart, Germany, local hope Philipp Kohlschreiber bowed out of the first round of the Mercedes Cup on Tuesday, falling to German compatriot Florian Mayer in straight sets.
The 35th-ranked Kohlschreiber was seeded sixth at the Stuttgart tournament but Mayer, ranked 21 spots lower in the ATP rankings, beat him 6-4, 6-2.
There was no such upset for fifth seeded Albert Montanes of Spain, who defeated Germany’s Philipp Petzschner 2-6, 7-5, 6-2 to advance to the second round.
Montanes’ compatriot Daniel Gimeno-Traver eliminated the defending champion Jeremy Chardy of France, 7-5, 6-7 (6), 6-3.
Also into the final 16 were Germans Bjoern Phau and Simon Greul, Spaniards Pablo Andujar and Guillermo Garcia-Lopez, and Argentina’s Juan Ignacio Chela and Horacio Zeballos, along with Gilles Simon of France.
In Prague, unseeded Monica Niculescu of Romania upset third-seeded Timea Bacsinszky of Switzerland 6-3, 7-5 to advance to the second round of the Prague Open.
Second-seeded Alexandra Dulgheru of Romania defeated Tathiana Garbin of Italy 6-4, 4-6, 6-2 Tuesday. Eighth-seeded Barbora Zahlavova Strycova stopped her Czech compatriot Andrea Hlavackova 6-2, 6-4.
Seventh-seeded Agnes Szavay of Hungary, fresh off winning her hometown Budapest title, also advanced with a 6-4, 6-3 victory over Liana Ungur of Romania.
Niculescu will face Czech Lucie Hradecka, who beat Stefanie Voegele of Switzerland 7-6 (8), 6-2.
Meantime, Serena Williams will miss the entire World TeamTennis season after cutting her foot.
The WTT said Monday she was to have played four matches for the Washington Kastles, but she hurt the bottom of her foot late last week and needed stitches.
It was not clear how she was injured. A message left with her publicist was not immediately returned.
Williams won her fourth Wimbledon crown this month and lost an exhibition to Kim Clijsters last Thursday before a record crowd in Brussels. She says she is “very disappointed” to miss the WTT season.
Her opening match was to have been last Friday against the New York Buzz in Glens Falls, New York She also will miss matches in Philadelphia on Tuesday, Washington on Wednesday and New York on Thursday.
