Celta Vigo 1-4 Real Madrid: Luka Modric with a wonderful goal
Karim Benzema gave Real the lead, but Iago Aspas equalised - both penalties following handballs - before Modric found the top corner from 25 yards from David Alaba's pass.
The Croatia midfielder, 36, then played a through ball to Vinicius Jr, who raced away and rounded goalkeeper Agustin Marchesin before slotting in.
Federico Valverde drilled in a fourth.
Real won a second penalty late, but Eden Hazard, who had only been on the pitch for a few minutes, saw his spot-kick saved by Marchesin. The former Chelsea player has only scored four goals in 50 La Liga appearances.
Madrid has won all three games this season, beating Eintracht Frankfurt in the Uefa Super Cup and Almeria on the opening day of La Liga.
Modric - who was applauded by the home fans when Dani Ceballos replaced him - has scored at least one league goal - in Bosnia, Croatia, England and Spain - every season since 2003-04.
Some 18 former Tottenham playmaker 33 La Liga goals have been scored outside the box.
Real Madrid left Casemiro out, with the Brazil midfielder, 30, close to a £70m move to Manchester United.
Young France midfielders Eduardo Camavinga and new signing Aurelien Tchouameni played alongside Modric in the middle of the park.
Carlo Ancelotti's side last lost a La Liga game to a team not from Madrid or Barcelona in January 2021.
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