The Danish side got off to a quick start as Sociedad narrowly escaped an early setback when Denil Castillo’s header from a pinpoint freekick clipped the left post.
The visitors soon gained control and Brais Mendez earned a penalty after Oliver Sorensen’s clumsy foul and coolly dispatched it into the bottom left corner.
The Wolves didn’t lose heart though, and pressed for a quick response, but Unai Marrero produced back-to-back stunning saves to deny Dario Osorio and Aral Simsir.
Just as Midtjylland began to grow into the contest, La Real swiftly doubled their advantage as Takefusa Kubo unleashed a thunderous strike into the top corner, curling in from the right flank in classic Robben-esque fashion.
However, Midtjylland halved the deficit before half-time when Adam Buksa capped off a slick team move with a close-range tap in at the near post, setting up a thrilling second period.
The visitors intensified their assault after the break, with Orri Oskarsson, Martín Zubimendi and Pablo Marin all threatening before the hour mark. Despite enjoying a month-and-a-half domestic break to fully focus on the UEL, Thomas Thomasberg’s men faced a formidable task in breaking down a resolute La Real side.
Instead, Midtjylland almost shipped in their third of the evening when substitute Mikel Oyarzabal forced a goal line clearance with 14 minutes to play.
The Wolves ultimately failed to net a second, leaving all to play for next week when they visit the Reale Arena in San Sebastián. The defeat marks their first of the new year and in three UEL games, having last fallen to FC Porto in mid-December.
Meanwhile, Real Sociedad claim just a second triumph in their last six competitive away games, reserving hopes of going deep into this season’s European second-tier tournament.