Steven Gerrard's side was flying at 3-0 thanks to goals from Alfredo Morelos, Joe Aribo and Nikola Katic, but the home side responded through Frank Onyeka and Sory Kaba.

However, Scott Arfield's cool finish 20 minutes from time gave Rangers a comfortable buffer ahead of the return fixture at Ibrox next week.

The visitor had been frustrated in their efforts until Morelos nodded home James Tavernier's wicked right-wing centre two minutes before the break.

Aribo finished a brilliant counter led by the dangerous Jordan Jones seven minutes after the restart and Rangers were cruising when Katic drilled home.

But Midtjylland fought back into the tie when Onyeka finished well on the spin two minutes later, while Kaba's edge-of-the-box effort further reduced the deficit.

Rangers kept coming, though, and Tavernier played a pass into the right channel for Morelos, who set up Arfield to provide a side-footed finish into the bottom-left corner. 

Gerrard's side will now look to complete the job when Midtjylland visit Glasgow on 16 August.