كتب : Hatem Maher
The Dutch winger scored the winner in the 31st minute after a brilliant individual effort.
He cut inside from the right, skipped past two challengers and curled a left-footed shot into the top corner of the net.
Real had to thank goalkeeper Iker Casillas for keeping their lead intact after saving two decent efforts from Giuseppe Rossi and Ariel Ibagaza in the second half.
French midfielder Lassana Diarra and Dutch striker Klaas-Jan Huntelaar, Real's winter signings, made their debut against Villarreal.
Real moved up to third in the league table with 32 points, one adrift of second-placed Valencia and a massive 12 behind leaders and arch-rivals Barcelona.