With four wins in a row in all competitions, Celta came into this as the form side and were intent on continuing their run five minutes in, when Borja Iglesias drilled a low effort from 20 yards, which forced Thibaut Courtois down low to keep it out.
But when Vinicius Junior got in behind and rolled an effort against the post soon after, the visitors found their rhythm, and after an Aurelien Tchouameni shot was deflected out for a corner, Real cleverly worked the resulting corner to the Frenchman, who swept in his first league goal of the season in the 11th minute.
Real had won all 18 previous LaLiga matches they had opened the scoring in this season, a record Iglesias seemed keen to end when he latched onto a through ball but was again denied by the fingertips of Courtois.
However, the striker would not be denied a third time, as on 25 minutes, Williot Swedberg brushed off Trent Alexander-Arnold on the left and squared for Iglesias to turn home the equaliser.
That goal seemed to put an end to the big chances before the break, until the 45-minute mark when Swedberg tested Courtois’ reflexes with a powerful side-footed shot.
Despite some intricate build-up play at both ends, it wasn’t until a corner to the near post was looped up into Courtois’ hands by Ferran Jutgla in the 60th minute that the second half had a shot.
Alvaro Arbeloa’s side finally showed some attacking intent soon after, as shots from youngsters Thiago Pitarch and Cesar Palacios were both well blocked by Carl Starfelt, before they were unfortunate not to be awarded a penalty for handball by Jutgla at a corner.
The Celta forward looked guilty as a lengthy VAR check took place, only for the hosts to be awarded a free-kick for a push by Palacios in the melee.
Los Blancos continued to have the majority of the late territory but weren’t turning it into chances, and came within inches of paying for that three minutes from time when Iago Aspas took aim inside the box and saw his effort bounce back off the post.
The Sky Blues looked to have held out and gone six unbeaten in all competitions, only for a poor clearance to fall to Valverde, whose strike from 25 yards to take a huge deflection on its way past Ionut Radu and win the game in the last minute for the visitors, who remain unbeaten in Vigo since 2014.
Flashscore Man of the Match: Thibaut Courtois (Real Madrid)