The team from Central Jutland was far from flawless, and the home side put up a spirited fight. However, the difference in quality told in the decisive moments, and the Danes returned home with a 2–0 victory from the first leg of the Conference League third qualifying round.
Franculino Djú put the visitors ahead in the first half, before Valdemar Byskov sealed the match with a fine free-kick goal after the break.
The visitors dominated possession in the first half but also conceded too many opportunities to the Irish home side.
Just past the 20-minute mark, the home team's Connor Parsons capitalized on a defensive error by Rasmus Nissen Kristensen, forcing Midtjylland goalkeeper Elias Olafsson to rescue his team with a crucial save.
That did not rattle the visitors, however. Shortly after, they took the lead when Sofus Johannesen delivered a precise cross into the box for Franculino Djú. Last season's Danish Superliga leading goalscorer was handed far too much space and responded with a cool finish inside the left post.
Bohemians continued to pose a threat at the other end, though.
After half an hour, the home side came close to carving out a clear-cut chance, but this time, captain Rasmus Nissen Kristensen stepped in well to make a decisive tackle.
Midtjylland lost further control of the game early in the second half, and fifteen minutes after the break, the visitors suffered a brief scare. Midtjylland's Denil Castillo attempted to clear the ball but instead struck an opponent in the head.
The referee pointed to the spot, but following a VAR check, the penalty was overturned because an offside had been called in the preceding passage of play.
After that scare, the Danes regained control of the match. With fifteen minutes remaining, the visitors won a free-kick on the edge of the box, and Valdemar Byskov capitalized on the opportunity to perfection.