Following the success, Madrid have now won 14 league matches in a row and will have the chance to match their record of 15 – set in 1961 – when they play Osasuna after the international break.
Well, it didn’t get easy anyway as Celta who finished 6th from the top of the Liga last season nearly frustrated the brilliant Los Blancos.
The home side won last season’s fixture 7-1 in March, but goals were not flowing as freely without injured attacking duo Cristiano Ronaldo – who scored four in that game – and Karim Benzema.
Morata, who rejoined Real in June after a two-year spell at Juventus, finished after Celta Vigo goalkeeper Sergio had parried Marco Asensio’s attempted chip.
The visitors quickly equalised through Fabian Orellana’s powerful finish.
But Madrid were not to be denied, with Kroos striking from outside the area with just nine minutes left to delight the Santiago Bernabeu.
The victory maintains Real’s winning start to the season after they defeated Sevilla 3-2 in the Uefa Super Cup and Real Sociedad 3-0 in their La Liga opener last weekend.
Barcelona will move above Real Madrid on Sunday if they beat Athletic Bilbao.
