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Rangers must win their final group game if they are to reach the last 32 of the Europa League despite holding Villarreal to a battling draw.
Steven Gerrard's side were reduced to 10 men just before the break when Daniel Candeias was shown a second yellow for a foul on Santiago Caseres.
Two superb Allan McGregor saves prevented Karl Toko Ekambi giving the visitors a deserved lead.
Glenn Middleton thought he had stolen a win for Rangers but was ruled offside.
Rapid Vienna's 2-1 comeback win away to Spartak Moscow had earlier ensured that Rangers would retain a chance of qualifying in the final round of fixtures no matter the result at Ibrox.
But, despite extending Villarreal's run of games in Scotland without a win to four, the Ibrox side finished the evening third in Group G, one point behind their Spanish and Austrian rivals.
The sides had shared a four-goal thriller in Villarreal at the start of the Group G campaign and it threatened to be another high-scoring affair with neither seemingly happy to settle for another draw.
Scott Arfield had an early chance from close range but stabbed his effort straight at visiting goalkeeper Andres Fernandez.
However, manager Javier Calleja had promised that Villarreal would press forward in search of a decisive win that would allow them to concentrate on pulling themselves clear of the La Liga relegation zone - and the visiting coach was true to his word.
McGregor has been Rangers' main man in their fine Europa League run and the Scotland goalkeeper was at it again, twice denying Toko Ekambi as the striker raced in on goal during long spells of Villarreal possession.
Rangers' tenacity forced the hosts back into the game and Connor Goldson lashed over from close range before the action boiled over in first-half stoppage-time.
With the home side angered not to have received a free-kick of their own, three Rangers players recklessly crashed into the back of Caseres.
Alfredo Morelos appeared to be the main culprit but, as Caseres rolled around holding his face, hesitant referee Matej Jug eventually ruled Candeias should be the one to receive his second yellow card.
The sending off forced Rangers to defend stoutly, but they limited Villarreal to a couple of long-range efforts before almost snatching the win themselves in a rousing finish.
Middleton was rightly ruled offside as he turned a James Tavernier cross in off a post and substitute Kyle Lafferty forced Fernandez to turn a blistering long-range effort over at full stretch.
Ramiro Funes Mori turned an effort over from close range late on, but the draw is enough to put the Spanish side top of the table.
Rangers have shown they can live with the three higher-seeded rivals in Europa League's tightest group, and determination and team spirit have been the watchwords.
This time, they had to do it against a side who have had a mini-revival in recent weeks - they are now unbeaten in six games, albeit five of them draws - and having to play 45 minutes with 10 men.
Gerrard this week insisted he still had some way to go before turning Ibrox into "a fortress" it once was. And, although they have now gone 15 games without defeat on home turf, their failure to beat Spartak and Villarreal in Glasgow - and a tendency to finish games a man short - could cost them dear.
They have now had six red cards this season - three in the Europa League - while it is the second time this month that Candeias has been given his marching orders.
Now they must lift themselves to new heights - of grit, skill and discipline - when they travel to Vienna on 13 December if they are to progress.
