Courtesy the victory, Real opened up a provisional three-point gap at the top. Real captain Sergio Ramos put the visitor in front at a rain-soaked Mendizorrotza Stadium by heading home a Toni Kroos free-kick after 52 minutes.
But he gave away a penalty from which Lucas Perez levelled in the 65th minute. Zinedine Zidane’s side demonstrated its new-found grit to retake the lead four minutes later. Isco pounced to head a Luka Modric cross against the post and the ball trickled across to Carvajal, who bundled it in from close range.
Alaves threw bodies forward in search of an equaliser but Real stood firm, with Marcelo blocking a goal-bound shot and goalkeeper Alphonse Areola stopping an effort from the host’s captain Manu Garcia in the eight minutes of added time.
Real provisionally leads the standings on 31 points from 14 games, ahead of holder Barcelona (28), which visits Atletico Madrid (25) on Sunday.
Liverpool extends lead in the Premier League
Liverpool hung on to a 2-1 win over Brighton & Hove Albion and extended its lead at the top of the Premier League to 11 points, thanks to a brace from Virgil Van Dijk.
Liverpool, which also equalled its unbeaten top-flight run of 31 games set between May 1987 and March 1988, has 40 points from 14 games, 11 more than second-placed Manchester City. The holder could only draw 2-2 at Newcastle United. Liverpool goalkeeper Allison was sent off in the final quarter of the game, but the host coped up well.
City dropped two vital points as Jonjo Shelvey hit a stunning strike late on to salvage a point for Newcastle. Kevin De Bruyne’s 82nd-minute thunderbolt looked to have won the game for City, which began the day nine points behind Liverpool.
Yet for the second time in the match, a resolute Newcastle mustered a quick response with midfielder Shelvey curling a shot past Ederson in the 88th minute. A 48th-minute goal from Aaron Cresswell earned West Ham United a surprise 1-0 victory at Chelsea, its first positive result since September.
Crystal Palace ended a winless run of five PL games with a 2-0 victory at Burnley.