- Sergio León (82')
- Karim Benzema (83' Pen, 89')
Ballon d'Or winner Benzema returned to the starting lineup after missing the World Cup for France, having suffered a thigh injury the day before the start, and had a big impact.
Real were awarded a penalty in the 83rd minute for handball by Javi Sanchez. The decision sent the home team into a frenzy and Leon was sent off for dissent. Benzema converted with ease.
The unmarked Benzema then doubled Real's lead in the 89th with a well-placed shot from inside the box after an assist from substitute Eduardo Camavinga.
There was a minute's silence before kick-off for Brazilian great Pele, who died on Thursday aged 82, with the country's former striker Ronaldo paying his respects in the stands.
"The clean sheet was good for us today," Courtois said. "In other games if you're winning 3-0, of course you want it, but I'd rather win 3-1 or 3-2 than a 0-0.
"Today it looked like being a draw for a long time, there were some good saves from both goalkeepers, we both played well. In the end, the handball, the penalty and Karim finished off the game for us."
- Kirkland: Madrid, Benzema show rust but return with win
Masip denied Vinicius Junior a goal with a reflex save from an acute angle after 17 minutes, with Benzema sending the rebound high over the bar from close range.
Courtois then made a brilliant save after 36 minutes when Alvaro Aguado tried a shot from the edge of the box towards the top left-hand corner and the Belgian kept it out one-handed.
Courtois had to save Real again in the 68th when he kept out Sergio Leon's header again with one hand.
"It was a difficult game against an opponent who got into the game little by little," Madrid boss Carlo Ancelotti said. "After the first half, when we did well, Valladolid played well and it was a competitive game.
"We didn't defend well, the team wasn't compact, but in this difficult situation we come away with three points, with a great game from Courtois, a great game from Benzema, so we end an unforgettable year well. We have players in different conditions and little by little we have to get them all into good condition."
Madrid have 38 points ahead of second-placed Barca, who host Espanyol on Saturday.
- José Luis Munuera Montero