Substitute Cho Gue-sung punished Nottingham Forest for their wasteful finishing with a late header to give Midtjylland the advantage in their Europa League last-16 tie.
Forest dominated large periods of the first leg in difficult conditions, as heavy rain and strong winds battered the players at the City Ground.
Murillo cleared a headed effort from Junior Brumado off the line in the opening stages before Forest took a firm grip on the match.
Elliot Anderson was the driving force from midfield, threading passes and joining up with attacks as Midtjylland struggled to get out of their own half.
Forest created numerous chances in a dominant opening 45 minutes, with Anderson, Igor Jesus, Ola Aina and Omari Hutchinson all testing goalkeeper Elias Olafsson.
Vitor Pereira switched from three in defence to a back four at half-time and Forest penned Midtjylland even deeper into their own half.
The chances continued to flow with Aina unlucky not to find the top corner when his own team-mate Morgan Gibbs-White blocked his close-range effort.
Substitute Valdemar Byskov was unlucky to see a left-footed strike crash off the crossbar in a rare attack by the visitors.
After the rain eased and Forest had spurned further chances through Nicolas Dominguez and Jesus, the Danish club seized their moment.
Cho was afforded too much space to meet a cross with his head and grab the visitors a valuable goal before next week’s second leg.