Mohamed Diomande's well-taken first-half strike saw Rangers beat Ludogorets 1-0 at Ibrox to earn Danny Röhl's side their first Europa League win of the season, but it was not enough to keep alive their play-off hopes.
The hard-fought victory over the Bulgarian champions did, however, maintain Rangers' recent good form as the home side racked up their seventh straight win in all competitions, including four clean sheets in a row.
Röhl has rejuvenated the Gers on the domestic scene since taking over from Russell Martin in October, but they went into the penultimate league phase fixture with just one point from 18 and effectively out of the competition.
However, on a wet and windy Govan night, midfielder Diomande put the home side into the lead in the 33rd minute and it proved to be decisive in a mostly controlled performance.
Rangers face Porto in their final Europa League fixture in Portugal next week, but first resume their Scottish Premiership title push at home to Dundee on Sunday.
The Light Blues are behind second-placed Celtic on goal difference and six points adrift of leaders Hearts, who host the Hoops on Sunday live on Your Site.
Your Site News reporter Adam Binnie:
There were valuable UEFA coefficient points up for grabs which could grant Rangers direct access to next season's Champions League should they go on to win the Scottish Premiership title.
Here's why.
The domestic league winner with the highest 'club coefficient' points total outside of Europe's top 10 leagues, calculated over the past five years, will qualify for next season's Champions League automatically.
Rangers currently hold that spot, largely down to their run to the Europa League final in 2022, but Olympiakos are hot on their heels.
Danny Röhl's side need a minimum of one point from their final match to hold on to top spot. They visit Porto next week.
Should Rangers fail to earn that point, Olympiakos could overtake them with a win at Ajax in their final game - remember they would also be required to win their domestic league.
It's important to note that Rangers are the only Scottish side who can benefit from this. Hearts and Celtic would have to play summer qualifiers if they win the league.
Rangers boss Danny Röhl:
"The first win in Europe is good for us as it keeps the momentum. Now seven wins in a row which is fantastic.
"Also from the last nine games, six clean sheets as well, this is great.
"But I also saw a lot of things to improve, and I think this is for me also the part, I will not close my eyes and say everything was nice. We know what we have to improve.
"We adjusted in the second half a little bit with our pressing which was more how I like.
"Then we created a lot of good opportunities and then we have to make it 2-0 or 3-0. We have this story very often, especially in these games.
"At half-time I said to them, 'guys, this is the big difference at the moment in the league and in Europe, we have clean sheets and if we have them, we have a chance to win games'.
"All in all, big respect to the performance of my players.
"It feels at the moment we can win, win, win, but it's always hard working, and it was the big message after the game.
"If we think on Sunday [against Dundee] we can go with 99 per cent, then we have not the chance.
"We need again 100 per cent during the next game, and this is the crucial thing. We have to demand of ourselves high standards, and this means we have to deliver every three days now 100 per cent to take wins."
