Rangers lost a European match at Ibrox for the first time under Steven Gerrard, as Bayer Leverkusen produced a classy performance to take control of their Europa League last-16 tie.
The German side dominated the opening 45 minutes and took a deserved lead through Kai Havertz's penalty, after a George Edmundson handball was spotted via VAR.
Rangers improved at the start of the second half, and Alfredo Morelos was denied by Lukas Hradecky, but Leverkusen soon extended their lead through Charles Aranguiz's stunning volley.
Edmundson brought Rangers back into the tie with a header from Ianis Hagi's corner, but Leon Bailey added a sublime third late on. Rangers will need to improve on their 2-1 win over Leverkusen in the 1998 UEFA Cup next week if they are to progress in the tournament.
The second leg will take place behind closed doors in Germany due to the coronavirus outbreak, but Ibrox was a sell-out, complemented by a lively contingent of away fans despite the concerns surrounding the evolving public health situation.
How Rangers fell to classy Leverkusen
Leverkusen had won eight of their previous nine games, and showed a desire to silence the home crowd inside two minutes, but Karim Bellarabi volleyed over when well placed.
Their technical superiority was clear to see as they dominated proceedings, while Rangers appeared content to sit in deep - but Gerrard's side were unable to keep the ball for any length of time when they had it.
There were a few anxious moments as first Edmundson and then Connor Goldson were forced to clear their lines deep inside their own box.
The speed of thought in Leverkusen's play left Rangers half a step behind throughout; Glen Kamara was booked for a late challenge on Mitchell Weiser which ruled him out of the second leg.
After 35 minutes Leverkusen were awarded a penalty following a VAR check, after Edmundson was adjudged to have handled Aranguiz's cross. Captain Havertz coolly sent Allan McGregor the wrong way from the spot to leave Ibrox stunned, but on the balance of play it was a deserved lead.
Joe Aribo had a shot blocked by Edmond Tapsoba as Rangers tried to respond, but they were receiving a lesson in dictating play from a team that had beaten Porto home and away in the previous round - at half-time, Leverkusen had 72 per cent of possession. The crowd was flat, and Rangers looked lifeless.
Gerrard made an early change in the second half, as Florian Kamberi replaced Aribo; Rangers' tempo was noticeably higher, and they soon had a sight of goal. James Tavernier drove forward and slipped the ball through to Morelos, whose powerful shot was superbly saved by Hradecky at his near post.
Ibrox was suddenly alive with noise, reacting to the improved endeavours of their team. Morelos nearly had a tap-in on 62 minutes after Kamberi pounced on a Leverkusen defensive mistake, but Jonathan Tah made a tremendous last-ditch clearance.
Leverkusen looked to have gone off the boil, but their attacking potency was underlined as they soon went 2-0 ahead. After Aranguiz's acrobatic effort was headed off the line by Steven Davis, Rangers failed to clear the resulting corner, and Aranguiz was given time in the box to hammer a low drive past McGregor.
Rangers could have wilted, but they grabbed a lifeline after 74 minutes as Edmundson was given the freedom of the six-yard box to thump a header in off the post from Hagi's corner. Three minutes later, Borna Barisic was inches away from a leveller, but his curling free-kick flew narrowly wide.
The outstanding Aranguiz came within inches of a second goal on the night from his own set-piece, which hammered off the crossbar with McGregor flailing helplessly. Rangers were hanging on, but with three minutes left they conceded what could be a crucial third, as Leverkusen turned on the style.
Moussa Diaby evaded two men on the right edge of the area and worked the ball left to substitute Bailey on the right corner of the box, who twisted inside Matt Polster before curling the ball high past McGregor. It was a moment of delightful quality that underlined the gulf in class between the sides, and left Rangers with a massive mountain to climb in Germany next week.
What the manager said...
Rangers boss Steven Gerrard: "They've got quality players, we know they're a good team. I think we had a rally good shape about us in the first half, but we showed them a bit too much respect.
"The penalty is a blow, but it is a penalty, because VAR is there, without VAR you might get away with it. In the second half we were more aggressive, more on the front foot.
"At 2-1, you're still thinking it's not the end of the world, but I'm extremely disappointed with the third goal.
"[The second leg] is going to be extremely tough, we knew it would be. But we've got a very important game at the weekend, we need to get recovered for that. We're disappointed to lose the game."
- This was Rangers' first home defeat in any European competition since 2011-12 Champions League qualifying (0-1 vs Malmo), ending a run of 17 games without a loss at Ibrox (W12 D5).
- Rangers have lost consecutive home games in all competitions for the first time since March 2018.
- Bayer Leverkusen have won consecutive away games in all European competition for the first time since October 2012.
- Having won none of their first 10 away games against British sides in all European competition (D3 L7), Bayer Leverkusen have now won their last two such matches, also beating Spurs 1-0 at Wembley in November 2016.
- Having failed to score or assist a single goal in his five Champions League appearances this season, Bayer Leverkusen's Kai Havertz has been involved in five goals in this three Europa League games this term (3 goals, 2 assists).
Rangers are due to play Celtic at midday on Sunday, live on Sky Sports Football, while the second leg of this tie will be played on March 19 at 5.55pm.
The Europa League quarter-final draw will take place in Nyon, Switzerland at 12pm on Friday, March 20