Vitor Pereira's side won 2-1 after extra-time at the MCH Arena in Denmark to level the tie at 2-2 on aggregate.

That set up the farcical shoot-out as Midtjylland's Cho Gue-sung and Aral Simsir both hit the post before Edward Chilufya slipped and blazed over in the shoot-out.

Morgan Gibbs-White, Ibrahim Sangare and Neco Williams converted Forest's three kicks to extend the club's first European campaign since 1995-96, when they reached the UEFA Cup quarter-finals.

The Premier League strugglers will play Porto or Stuttgart in the quarter-finals.

Admitting he needed his players to be "fresh mentally and and physically", Pereira prioritised Sunday's vital clash with relegation rivals Tottenham as he made nine changes from last weekend's 0-0 draw against Fulham.

Pereira's understudies rose to the challenge, with Lorenzo Lucca's close-range strike repelled by Elias Olafsson before Ryan Yates slammed a half-volley against the bar from 10 yards.

Lucca's header was hacked off the line by Philip Billing and moments later the Italy forward lashed over with only Olafsson to beat.

James McAtee's low drive from distance was parried by Olafsson, but Forest's pressure was finally rewarded from the resulting corner in the 41st minute.

Rising to meet Nikola Milenkovic's flick, Nicolas Dominguez craned his neck to loop a header over Olafsson from six yards.

- Celta advance -

Beaten just once at home in all competitions this season, Midtjylland had no answer to Forest's relentless pressure and the visitors struck again in the 52nd minute.

McAtee found Yates 25 yards from goal and the Forest captain smashed a superb strike past Olafsson.

Midtjylland dragged themselves back into the tie completely against the run of play, Martin Erlic blasting home from just inside the area in the 69th minute.

Celta Vigo beat nine-man Lyon 2-0 in France to secure a 3-1 aggregate win.

Lyon, who finished top of the league phase, were reduced to 10 men in the 19th minute when Senegal defender Moussa Niakhate was sent off for a foul on Javi Rueda.

Rueda, who also netted in the first-leg, ensured the Spanish side took advantage of their numerical superiority with a close-range finish in the 61st minute.

Ferran Jutgla scored in stoppage time to wrap up the victory before Lyon's Nicolas Tagliafico was dismissed for a second booking.

Celta will play Freiburg for a place in the semi-finals after the German side crushed Genk 5-1 to secure a 5-2 aggregate victory.

Matthias Ginter put hosts Freiburg ahead in the 19th minute and Igor Matanovic doubled the advantage six minutes later.

Genk's Matte Smets netted in the 39th minute, but Freiburg put the result beyond doubt thanks to Vincenzo Grifo's 53rd-minute strike and a Yuito Suzuki goal three minutes later.

Maximilian Eggestein completed Freiburg's rout in the 79th minute.

Later on Thursday, Aston Villa will defend their 1-0 first-leg advantage against Lille, while Roma and Bologna are level at 1-1 in the all-Italian clash.

Porto are 2-1 up from the first leg against Stuttgart, and Real Betis will seek to overturn a 1-0 deficit at home to Panathinaikos.

Sporting Braga booked their last-eight place with a 4-0 victory over Ferencvaros in the second-leg on Wednesday.