By Clive Lindsay
Rangers captain Barry Ferguson worked hard in midfield
Goalkeeper Allan McGregor was Rangers' hero, twice denying Igor Burzanovic during the opening 45 minutes.
Dusan Andjelkovic sliced over and then forced McGregor into another save.
Jean-Claude Darcheville and Lee McCulloch went close for Rangers after the break, while McGregor denied Ognjen Koroman to preserve the aggregate lead.
It was some revenge for Rangers following the 3-0 defeat suffered in Belgrade in 1990, when Red Star went on to win the European Cup.
The Serbian champions' present line-up is not of that quality and were unable to break down a Rangers side determined to protect the 1-0 lead given them by Nacho Novo's late winner at Ibrox.
Brahim Hemdani, McCulloch and Darcheville had been promoted to Rangers' starting line-up, with DaMarcus Beasley, Kris Boyd and Daniel Cousin dropping out of the side that defeated Kilmarnock.
Red Star had Dusan Basta and playmaker Burzanovic back in their team.
Jean-Claude Darcheville (right) was a lone man up front
And Burzanovic almost made an immediate impact after Rangers' 4-5-1 formation was breached within seconds of kick-off.
Carlos Cuellar missed his attempt at a headed clearance then slipped - and the Red Star playmaker's shot was blocked by McGregor from point-blank range.
Darcheville claimed for a penalty when tackled by Ibrahima Gueye, but referee Lucilio Batista decided that the ball was won cleanly.
Rangers threatened again when Darcheville's power saw him find space on the right, but Ferguson could only fire wide of the near post from his cross to the near post.
McGregor made a decent block just after the half-hour point of the game.
Burzanovic burst into the penalty area and drove a shot from the right of goal towards the far corner, but McGregor pushed the ball to safety.
MY SPORT: DEBATE It would be churlish to deny that Rangers are now looking like a good side under Smith
Macaroons
Red Star should have gone ahead when Filip Dordevic's shot was deflected into the path of Andjelkovic, but the defender sliced his right-footed volley well over the bar from 14 yards.
McGregor kept Rangers ahead in the tie with another save from a goal-bound drive from 15 yards by Andjelkovic.
Darcheville had a chance to virtually kill-off Red Star's hopes after 56 minutes when he wriggled clear but drove the ball wide of the far post from the edge of the box.
Red Star goalkeeper Ivan Randjelovic had to get down swiftly to push a McCulloch drive wide after the Rangers midfielder made room for himself 20 yards out.
McGregor matched that and more when he turned a blistering 25-yard effort from Koroman over the crossbar.
And Rangers saw out the remaining minutes to move into the group stages via toil rather than aplomb.
Crvena Zvezda: Randjelovic, Andjelkovic, Milijas, Koroman, Burzanovic, Tutoric, Lucas, Gueye, Basta, Dordevic, Castillo.
Subs: Banovic, Barcos, Bronowicki, Bajalica, Molina, Raskovic, Milovanovic.
Rangers: McGregor, Hutton, Weir, Papac, Whittaker, Hemdani, Thomson, Cuellar, McCulloch, Ferguson, Darcheville.
Subs: Carroll, Boyd, Novo, Beasley, Broadfoot, Webster, Cousin.
Referee: Lucilio Cardoso Cortez Batista (Portugal)
survived a testing match in Belgrade to progress through to the group-stages of the UEFA Champions League.

 was Rangers' hero twice in the opening 45 minutes denying  striker, , twice in the first half.

 and  shot close for Rangers in the second half, whilst McGregor denied  to preserve the 0-0 draw, and the 1-0 lead on aggregate.
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