The visitors stunned the German giants when James Tavernier’s penalty was followed by Alfredo Morelos’ tap-in.
John Lundstram’s fantastic strike made it three, but Jude Bellingham replied instantly with a fine drive of his own.
Dan-Axel Zagadou’s own-goal restored the three-goal lead before Raphael Guerreiro gave Dortmund a lifeline.
The game’s first five goals came in an astonishing 16-minute spell across the end of the first half and the start of the second period, as Rangers continually sliced through a fragile Dortmund side who currently sit second in the Bundesliga.
Despite there being only 10,000 fans in attendance because of Covid restrictions inside the iconic cauldron of the Signal Iduna Park, the home crowd made their feelings clear as the pocket of delirious travelling fans celebrated throughout the game and on after the final whistle.
The return leg of the play-off knockout round tie will take place at Ibrox next Thursday.
The absence of 21-year-old striker Erling Haaland, who has 23 club goals in 20 games this term, coupled with the subdued home crowd would have provided Giovanni van Bronckhorst’s men and their travelling following with crumbs of positivity for what was expected to be a daunting trip to Dortmund.
But even without their in-demand striker, the Bundesliga side’s starting line-up was still littered with top-level European talent.
The attacking trio of captain Marco Reus, Julian Brandt and England’s teenage sensation Bellingham, who were all playing behind Dutch international striker Donyell Malen, highlighted the attacking power the hosts possessed.
But it was the Scottish visitors, who settled quickly at the Signal Iduna Park, asking the early questions.
Van Bronckhorst’s men were composed in possession and very nearly had a deserved lead when Ryan Kent slipped in Borna Barisic on the left of the box, but the Croatian’s low finish was saved by the foot of Dortmund keeper Gregor Kobel.
However, Rangers’ impressive opening was almost undone with slack defending when a home corner found Zagadou free, but the defender failed to make a clean enough connection with his downward header.
That missed opportunity seemed to briefly spark life into Dortmund, who saw a sweeping passing move end with Reus nicking the ball wide when leaving it for Malen was the better option.
But Rangers survived to bag two goals in a sensational three-minute spell which stunned the home crowd. Tavernier started it off as he sent Kobel the wrong way with a well-taken penalty after a VAR check spotted a clear handball in the box from Zagadou.
And it was two moments later when Joe Aribo flicked on Tavernier’s corner, leaving Morelos to tuck the ball away at the back post.
The manic nature of the game would continue into the second half as outstanding work from Kent on the left helped tee-up Lundstram, who wrapped his left foot around the ball to add a stunning third.
Dortmund raced up the other end in a breathless start to the half to reduce the deficit when Bellingham bent in a fine effort of his own, but Rangers’ remarkable lead was back to three in as many minutes.
Aribo slipped in Morelos on the left, who had a strike that was trailing wide. However, it took a nick off Zagadou and rolled into an empty net. The goal was momentarily ruled out, but a quick VAR review saw no issue with it.
Rangers continued to trouble a weak backline, with World Cup-winning centre-back Mats Hummels at the heart of it, as Aribo’s fierce strike whistled past the far post.
But on a night of fine strikes, it was Dortmund who had the last say when Guerreiro’s dipping effort left Allan McGregor, making his 100th European appearance, rooted to the spot.
What the stats say
- Borussia Dortmund conceded four goals in a home European match for only the third time in their history, also doing so in November 1964 vs Man Utd (lost 6-1) and November 2016 vs Legia Warsaw (won 8-4).
- In the Europa League (since 2009-10), only one side has ever won the first leg of a knockout tie by 2+ goals away from home and then not gone on to qualify: Real Betis vs Sevilla in 2013-14 (won 2-0 first leg, lost 2-0 second leg, lost on pens).
- Borussia Dortmund have conceded 4+ goals in consecutive home games in all competitions (2-5 vs Bayer Leverkusen, 2-4 tonight) for the first time since May/June 1983 (4-4 vs Bayern Munich, 4-6 vs Borussia Mönchengladbach).
- Rangers ended a run of eight away European matches in Germany without a win (D1 L7), with this their first since a 2-1 win over Bayer Leverkusen in the Uefa Cup in October 1998, a match which saw current manager Giovanni van Bronckhorst score the opening goal for the Gers.
- Alfredo Morelos became the all-time leading scorer for Rangers in major Uefa European competition (the competitions: European Cup, Champions League, Cup Winners’ Cup, UEFA Cup and Europa League) with 14 goals, overtaking Ralph Brand’s record of 13 goals between 1960 and 1964.
- All four of James Tavernier’s Europa League goals have been scored from the penalty spot – his opener was his eighth goal of the season for Rangers in all competitions, with only Morelos (16) and Kemar Roofe (11) scoring more.
- Before Van Bronckhorst’s arrival this season, Morelos had scored six goals in 19 appearances in all competitions for Rangers – under the Dutchman, he has scored 10 times in 12 games, twice as many as any other player in that time.