The homegrown striker ending that eight-year streak will come as a welcome relief to Madrid, who have been criticised in previous seasons for not giving development opportunities to their own young talent in favour of star buys from overseas.
Morata made the most of just his 10th league start of the season, scoring three times in Madrid's dramatic 4-2 victory away to Leganes on Wednesday.
The former Juventus striker netted Madrid's second and third goals of the night with a looping header and a confident first-time finish, two goals that ensured he reached 10 top-flight strikes for the first time in his career.
And he got his third three minutes into the second half to seal the visitors' victory, the Spain international credited with the goal despite his close-range header taking a huge deflection off Leganes defender Martin Mantovani, who bizarrely had his hands raised.
Club legend Raul was the last Spanish star to score league hat-trick for Madrid against Sevilla eight years ago – he scored a treble in a 4-2 win at Ramon Sanchez Pizjuan.
Zinedine Zidane rested Cristiano Ronaldo and Gareth Bale for the game, while Karim Benzema was an unused substitute.