Modric curled home from outside the box just before half-time to put Carlo Ancelotti's side back in front after Karim Benzema's early penalty had been cancelled out by Iago Aspas, who converted a spot-kick at the other end.
Vinicius Junior and Federico Valverde added further goals in the second half while Eden Hazard had a late penalty saved as Madrid built on their La Liga season-opening 2-1 win at Almeria and joined Real Betis and Osasuna on six points at the top of the fledgling standings.
Real took the lead inside the opening quarter of an hour at Balaidos, Benzema slotting in a penalty after the referee penalised Celta's Peruvian midfielder Renato Tapia for handball following a VAR review.
Yet Celta won a penalty of their own midway through the first half as Eder Militao blocked a Goncalo Paciencia header with his arm, and veteran striker Aspas -- who scored 18 times last season -- made no mistake from the spot.
Franco Cervi then crashed a shot just wide as Celta threatened to go in front against a Real side playing their first game since agreeing to sell midfielder Casemiro to Manchester United.
However, Modric was back in the starting line-up and made it 2-1 three minutes before the interval, collecting possession in space 25 metres from goal and advancing before curling a tremendous shot high into the net from the edge of the D.
Real's class told after the break, as Modric sent Vinicius away to round goalkeeper Augusto Marchesin and slot in the visitors' third goal in the 56th minute.
It was 4-1 before the midway point in the second half, with Vinicius trying to pick out Benzema only for the Frenchman to slip, allowing the arriving Valverde to plant a low first-time shot into the far corner.
It could have been worse for Celta as Madrid won another penalty late on when Benzema was fouled in the box by Hugo Mallo.
Benzema left the spot-kick for Hazard, who had come on as a substitute, but the Belgian's kick was saved by Marchesin.
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