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.

Tencent confirmed that up to six former employees were under investigation in an ongoing anti-graft probe.
China's biggest social network said an "internal investigation" brought to light bribery allegations.
Several executives have been implicated in China's corruption crackdown.
The government has been on a drive to reform the economy, the world's second largest, by clamping down on corruption in major institutions and businesses for the past two years.
Tencent has not identified the former employees, but said that "the police have been notified" and they were awaiting further information.
Alibaba confirmed to the Reuters news agency that Mr Lui was detained but the case was "related to his time at Tencent and has nothing to do with Alibaba".
Mr Liu left Tencent for competitor Alibaba in 2013 to become the president of its digital entertainment unit.
Tencent is behind China's popular messaging app, WeChat. It also owns China's largest music streaming service by subscribers and its online gaming business has been compared to that of Nintendo's and Sony's gaming units.
Alibaba also has a large stake in Weibo, a social media site similar to Twitter as well as Chinese online video providers similar to YouTube.
China's anti-corruption crackdown has targeted both government officials as well as company executives with many being taken into custody.
Among recent high-profile cases in the past year were China's ex-security chief Zhou Yongkang and the former China head of pharmaceutical firm GlaxoSmithKline Mark Reilly.

Called The Highlands and Islands Creative Campus, it has been created at Blair Steading on the Altyre Estate near Forres in Moray.
GSA describes it as a research and postgraduate teaching centre for "international excellence in creativity and innovation".
Highlands and Islands Enterprise has been supporting the creation of the campus.
The site is a base for GSA's Institute of Design Innovation.
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.
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Chinese e-commerce giant Alibaba has said its senior executive Patrick Liu is in police custody over corruption allegations related to his previous job with internet company Tencent.
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Glasgow School of Art (GSA) has formally launched a new campus.