Substitute Ivan "Riki" Sanchez headed wide just before halftime for Deportivo, who started former Spain international Juan Carlos Valeron in a league game for the first time in three years.
Robben created a good chance in the 58th minute when he burst down the right side before sending a shot just over the far corner, while Iker Casillas was called into action at the other end a minute later with the Madrid goalkeeper making a good save from Filipe Luis' well struck shot.
The Spain goalie dove to his right in the 68th minute to save Angel Lafita's rising shot to maintain Madrid's lead and condemn Deportivo to a fifth straight loss in all competitions.
At La Rosaleda, John Heitinga scored in the 45th as Atletico Madrid rallied for a 1-1 draw at Malaga, which got its goal from Antonio "Apono" Galdeano in the 22nd. Atletico's Simao Sabrosa had a shot cleared off the goal line in the 69th and Malaga goalkeeper Inaki Goita saved Tomas Ujfalusi's close-range header in injury time as both teams moved to 32 points.
Atletico remained winless in 2009, a stretch of six games.
Also yesterday, it was: Almeria 2, Athletic Bilbao 1; Valladolid 1, Espanyol 1; Recreativo Huelva 1, Real Betis 0; and Getafe 5, Sporting Gijon 1.
Somber music was played before the games as a mark of respect for the four children killed Saturday when part of a Barcelona sports center collapsed in high winds.
Coach Hugo Sanchez's unbeaten reign at Almeria was stretched to four games. Irney Santos da Silva's blast came directly off the bar to Juanma Ortiz to head home in the 26th, and Kalu Uche then struck a loose ball through the crowded area in the 40th.
Joseba del Olmo got one goal back for Athletic in the 66th.
At Valladolid, Sergio Sanchez's 79th-minute header ensured Maurecio Pochettino came out of his Espanyol league coaching debut with a point, although Espanyol stayed winless in 11 games to drop into 19th.
Henok Goitom steered Jonathan Sesma's shot home with his head in the 42nd for Valladolid.
Roberto Soldado scored a hat trick as Getafe snapped a four-game losing streak. Soldado jumped on a poor back pass in the 15th to beat Sporting goalkeeper Inaki Lafuente, running clear onto a Ikechukwu Uche pass to score in the 57th and then notched his sixth of the season with a penalty in the 72nd.
Esteban Granero and Uche also scored for Getafe, while David Barral scored Sporting's goal off a quick counterattack in the 45th.
Roberto Abbondanzieri watched his last Getafe game from the bench with the Argentine goalkeeper returning to Boca Juniors later this week.
At the Nuevo Colombino stadium, Javier Camunas headed Cristian Maidana's cross over Betis goalkeeper Ricardo Soares for Recreativo's 72nd-minute winner. Recreativo stretched its unbeaten run to five and has 23 points.
On Saturday, Osasuna rallied to draw 1-1 against Villarreal.
(Agencies via Shanghai Daily January 26, 2009)
