The Netherlands winger came inside from the right and shimmied across the penalty area past several challenges before curling a hard shot into the far top corner, leaving Diego Lopez with no chance.
Former Portsmouth midfielder Lassana Diarra and Netherlands striker Klaas-Jan Huntelaar made their debuts for Real but both were substituted in the second half after playing small roles in the win.
With both teams on 29 points before the start of the match, a win for either would have seen them go third behind Valencia, who like leaders Barcelona were winners on Saturday.
There were several chances at either end, with Iker Casillas pulling off a sensational fingertip stop from a close-range Giuseppe Rossi header in the second half.
Sevilla 1-1 Osasuna
Sevilla missed the chance to go back above Real and Valencia into second as Walter Pandiani's 91st-minute equaliser earned Osasuna a 1-1 draw at the Ramon Sanchez Pizjuan.
Osasuna were the better side in the first half, but Sevilla took the lead after 50 minutes when Jesus Navas chested down on the edge of the box before firing an unstoppable volley into the far bottom corner.
The edgy home fans saw Fredi Kanoute miss a golden chance with his head in the first half.
The Malian, who had a tee-shirt with the word 'Palestine' written upon it visible under his rain-soaked Sevilla shirt, could have snatched the points when another header four minutes into injury-time was diverted on to the crossbar by visiting goalkeeper Roberto.
Having missed the chance to display his message regarding the Israeli-Palestinian conflict, Sevilla remain fourth in the table.
He also denied the creator of that chance, substitute Ariel Ibagaza, with a save low to his left.
Another sub, Joseba Llorente, was prevented from levelling by the Spain shot-stopper after wasting a pair of other chances.
Robben hit the woodwork for Real after 12 minutes, his shot from outside the box after a driving run deflected by a diving Gonzalo Rodriguez on to the bar and over.
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