Williot Swedberg struck twice in the second half for Celta, with Madrid’s second league defeat of the season leaving rivals Barcelona four points clear at the top of La Liga.
Xabi Alonso’s side, second, also lost defender Eder Militao to injury on a difficult night in the Spanish capital.
Madrid were playing their first match at home following six on the road across all competitions after hosting an NFL match at the Bernabeu, coinciding with a poor run of form, having now won just one of their last five league games.
“(This was) tremendous. We read the game very well, we had some luck in the chances that we had, but we did well,” Celta striker Borja Iglesias said.
“With the team they have and their quality, it’s hard to equal them, but we read it well, we had the ball, we played in their half, we played a great game,” he added.
With a juicy Champions League clash against Manchester City and Erling Haaland approaching on Wednesday, Alonso chose to rest centre-back Antonio Rudiger, starting with Carreras in the heart of defence.
Rudiger’s break did not last long, with the German defender coming on midway through the first half after Militao pulled up injured.
Raul Asencio started at right-back, after Trent Alexander-Arnold was sidelined for two months with a thigh injury, continuing a tough start to life in the Spanish capital for the former Liverpool defender.
Celta Vigo goalkeeper Ionut Radu made a handful of good saves in the first half, keeping out a Jude Bellingham header and Arda Guler’s drive from range.
Madrid were struggling to create serious danger as Celta set up in a tough-to-crack low defensive block, denying dangerous forwards Kylian Mbappe and Vinicius Junior space.
Guler missed Madrid’s best chance of the first half, with the Turkish playmaker sending a shot wide on the swivel after Mbappe teed him up.
Radu also thwarted Vinicius after Aurelien Tchouameni chopped a ball in behind the defence for the Brazilian to run onto, a rare crack in Celta’s armour.
Celta’s Romanian goalkeeper turned away a fierce Fede Valverde effort from distance early in the second half, before Celta stunned the hosts.
Bryan Zaragoza crossed from the left for Swedberg, who produced a gorgeous flicked finish to beat Thibaut Courtois to send the Galicians ahead. (AFP)