Real - who have won 29 of those 38 matches - are one short of equalling a best-ever run by a La Liga team.
James Rodriguez scored twice as he made a rare start in the absence of the rested Cristiano Ronaldo.
Raphael Varne also headed home to put Real firmly in control with the second leg in Seville on 12 January.
It is a second leg which now appears a formality amid a hectic schedule that could see Real play 21 times in 11 weeks.
Madrid started a second consecutive home game without any of their first-choice front three with Karim Benzema on the substitutes' bench, Ronaldo rested and Gareth Bale sidelined with a long-term ankle injury.
Rodriguez had previously said he would consider his future in January after playing a minor role so far this season, but made the most of a rare start by scoring a spectacular long-range opener and adding his second from the penalty spot after Luca Modric was fouled by Mariano.
Real Sociedad also took a huge step towards the last eight with Willian Jose, Carlos Vela and Mikel Oyarzabal scoring in a 3-1 win over Villarreal.
Real Madrid extended their unbeaten run to 38 games with a 3-0 victory over Sevilla in the first leg of their last-16 Copa del Rey tie at the Bernabeu.