Real smash Sporting to cut Barca's lead
Raul's goals made him Real's all-time top scorer, surpassing Alfredo di Stefano's tally by two to move on to 309 goals for the nine-times European champions.
Real's eighth consecutive victory put them on 50 points from 23 matches.
"We are closer (to Barcelona) because we have hauled back two points but it is still very difficult. It is out of our hands and we have to wait and see what happens," Real coach Juande Ramos said.
Sevilla climbed up to third with 41 points after two goals in the last six minutes from Frederic Kanoute earned them a 2-0 win away to bottom club Espanyol.
The Mali striker put away two Jesus Navas crosses against Espanyol, who played the last 25 minutes with 10 men.
Valencia are fourth with 38 points, ahead of Villarreal on goal difference, after drawing 1-1 at home with Malaga on Saturday.
Villarreal were held 1-1 away to Racing Santander on Sunday, and Atletico Madrid are sixth with 36 points after Juan Albin, who had earlier missed a penalty, scored a late goal for Getafe to draw 1-1 at the Calderon.
Real Madrid were without the injured Arjen Robben at the Molinon but his absence was quickly forgotten as Raul stroked in Sergio Ramos's cross after 15 minutes.
Juande Ramos gave new signing Huntelaar a rare start and the Dutch striker returned the favour with his debut goal for the club, beating Inaki Lafuente in the one-on-one after a flick on from Gonzalo Higuain before the break.
Higuain set up the third just after the re-start back-heeling to set Marcelo clear on a counter-attack, and the Brazilian international calmly lifted the ball over Lafuente.
Sporting's keeper gifted Raul the fourth when he let Higuain's shot squirm through his legs for a simple tap-in 14 minutes from time, and the home side's best chance came when David Barral lashed a shot against the post at the end.