Alfredo Morelos became Rangers' top European goalscorer but Darwin Nunez's injury-time strike saw 10-man Benfica snatch a 3-3 draw in the Europa League.
Morelos's tap in six minutes after half-time - the Colombian's 22nd goal in Europe seeing him overtake Ally McCoist as Rangers' leading scorer on the continent - had given his side a 3-1 lead, only for the Portuguese to hit back twice in the final 13 minutes through Rafa Silva and substitute Nunez.
Rangers had made the worst possible start when falling behind after only 60 seconds thanks to Connor Goldson's unfortunate own goal, only for Nicolas Otamendi's straight red card (19) to then turn the game on its head as the visitors scored twice in just 88 seconds.
Steven Gerrard's side levelled matters through Diogo Goncalves's own goal (24), before Glen Kamara immediately made it 2-1 with his first strike since September 2019.
Nunez's late effort means both teams remain unbeaten and at the top of Group D ahead of the return meeting at Ibrox.
Benfica: Vlachodimos (6), Goncalves (7), Otamendi (5), Vertonghen (6), Tavares (6), Weigl (6), Rafa Silva (8), Pizzi (7), Taarabt (6), Everton (6), Seferovic (5)
Subs: Gilberto (6), Grimaldo (6), Nunez (8), Waldschmidt (6), Jardel (6)
Rangers: McGregor (6), Tavernier (8), Goldson (6), Helander (5), Barisic (7), Jack (7), Davis (8), Kamara (8), Aribo (7), Kent (7), Morelos (9)
Subs: Arfield (7)
Man of the match: Alfredo Morelos
How Rangers failed to beat 10-man Benfica
Rangers arrived at the Estadio da Luz knowing that no team had beaten Benfica at home in the Europa League and that task became even harder when they fell behind to the fastest own goal in the competition in more than a decade.
The normally reliable Filip Helander failed to clear his lines, allowing Silva to get in behind, with his pull back ending up in the net off Goldson's thigh.
But Benfica soon handed Rangers a way back. Steven Davis's wonderful ball over the top released Ryan Kent, only for Otamendi to trip the midfielder's heels as he bore down on goal, leaving the referee with no choice but to send off the former Manchester City defender.
Rangers took full advantage by first levelling matters when Goncalves diverted James Tavernier's driven centre into his own net, before Kamara then rounded off a lovely passing move to hand his team a deserved half-time lead.
Benfica made four changes from their last league outing, while Rangers boss Steven Gerrard made two changes from the side that won 1-0 at Kilmarnock on Sunday, with Glen Kamara and Steven Davis replacing Scott Arfield and Cedric Itten.
The visitors soon increased their advantage when the unmarked Morelos side-footed home another Tavernier cross for his record-breaking 22nd European goal in just 37 games, and all this from a player who cost the club just £1m.
However, if Rangers thought they had become the first-ever team to win a Europa League game at Benfica, they were mistaken, with the home side showing great character to snatch a point late on.
First Silva converted after fine approach play from Nunez, before the substitute himself was played clean through on goal in stoppage time, keeping his cool to break Rangers hearts.
'It will feel like defeat for Rangers'
Sky Sports' Kris Boyd:
"Rangers' game management has really improved in Europe under Steven Gerrard, but I didn't know what they were doing in the last five minutes against Benfica. They got caught, they were sloppy and that allowed Benfica to create the opportunity to equalise.
"Rangers were heading for a big performance and a big result, but it probably feels like a defeat now. With Benfica down to 10 men, Rangers were in total control, but somehow, they managed to draw it.
"It's a disappointing result, though I'm sure Gerrard would have taken a 3-3 draw if it was offered to him at the start of the night. There are a lot of positives to take - Alfredo Morelos passing Ally McCoist's record with his 22nd European goal - but drawing having dominated from 20 minutes onwards will have really annoyed Gerrard."
Opta stats - No place like home for Benfica
- Benfica remain unbeaten in all 24 of their UEFA Europa League home games since the competition was rebranded in 2009, winning 19 and drawing five.
- Rangers conceded three goals in a match for the first time in 20 games in all competitions (1-3 vs Bayer Leverkusen in March). Indeed, they shipped more goals tonight than they had in their previous nine games in all competitions combined (2).
- This was the fourth different UEFA Europa League game to see both sides net an own goal, with half of these now involving Rangers (vs Benfica tonight, and vs Spartak Moscow in November 2018).
- Alfredo Morelos scored his 10th UEFA Europa League goal for Rangers, the first player to reach double figures in the competition for the Scottish side (including UEFA Cup).
What the manager said...
Steven Gerrard: "That will certainly sting for a while. It obviously feels more like a defeat than a positive point right now. But once the dust settles I'm sure it will be a valuable point.
"We've got ourselves to blame. We started the game really poor for the opening minute and deserved to be one behind. We also finished the game poorly as well, so we certainly have a lot to learn from the goals we conceded.
"Having said that, once the red card happened some of the football and some of the creativity we produced and the goals we scored were absolutely fantastic. I thought there were periods in the game where we actually played the best we have this season.
"It's certainly very mixed at the moment. It feels like a defeat because at 3-1 our game management and our order on the pitch should have been better to get us over the line."
Man of the Match - Alfredo Morelos
The forward made history in Lisbon with a simple far-post finish, the Colombian's 22nd European goal, more than any other player has managed in Rangers' history, while he has also now netted 84 times in total in just 154 games for the club.
However, it was not just that record-breaking strike that caught the eye at the Estadio da Luz, but the frontman's all-round game, including a brilliant crossfield pass to assist Kamara's 25-minute goal.
And really he could have had more in the second half but for some alert goalkeeping by Odysseas Vlachodimos, although in the end all people were talking about was his second-half goal that leaves him top of pile in Europe as far as Rangers are concerned.
Benfica entertain Braga on Sunday at 8pm, while Rangers take on Hamilton at Ibrox in the Scottish Premiership on the same day, with the game kicking off at 3pm.