With a 3-0 lead to hold onto Rangers had one foot in the last eight but knew it would not be easy in the hostile Marakana.
And so it transpired, a tenth minute opener sliced into their advantage with some defensive hesitancy at an early corner kick and Allan McGregor was called upon to make a number of important saves in the first and second halves of the game as Red Star pressed the Scottish champions hard.
Red Star had somehow transpired to leave Glasgow without scoring and though they breached McGregor’s goal through Mirko Ivanic’s opener, the Rangers goal did lead another charmed life with the 40-year-old keeping Rangers in it as he so often does on the European stage.
However their fight evaporated when Ryan Kent restored the three-goal cushion with a sprint and strike on 56 minutes which levelled on the night and sent Rangers 4-1 up on aggregate, an advantage they would not relinquish even though Ben Nabouhane scored a late penalty for the home side.
Here's how Giovanni van Bronckhorst’s hard-working side rated as they earned their place among the Europa League’s last eight – the only national champions left in the competition...
1. Allan McGregor - 9
Last week's penalty hero made two vital stops in the first half - but had no chance for the goal having stayed on his line for the corner. Continued that in the second half with some incredible reaction saves. Photo: Ian MacNicol
2. James Tavernier - 7
Right-back playmaker took up both roles as per usual, and Belgrade rarely made progress on his flank - while Rangers often did. Even more of a threat going forward once Arfield entered on the right of midfield. Photo: Ian MacNicol
3. Calvin Bassey - 7
Has come of age this season and charged forward with confidence and defensively strong. Could even have had a goal with a twisting charge into the box in the first half but crowded out before he could decide to shoot or pass. Photo: Craig Foy - SNS Group
4. Leon Balogun - 7
Defender scored the third last week but never threatened in Serbia. Some stress relieving runs out of defence with the ball lifted pressure and when the heat was on, defended resolutely. Photo: Craig Foy - SNS Group