Giovanni van Bronckhorst‘s men backed up their stunning win over Borussia Dortmund in the play-off round with another dominant first-leg performance against Red Star at Ibrox.
Rangers captain James Tavernier opened the scoring from the spot, before Alfredo Morelos smashed home on a set-piece.
Veteran goalkeeper Allan McGregor came up big in Europe again as he saved Aleksandar Katai’s penalty, diving low to his right for a stunning stop and centre-back Leon Balogun powered home a header on a second-half corner to put his team firmly in the driving seat.
Eliminated in the last 16 in each of the last two seasons, Scotland’s champions now stand on the verge of the quarter-finals after a 3-0 rout of Red Star Belgrade at Ibrox.
Red Star saw three goals correctly ruled out for offside but were fuming about the penalty awarded for a foul on Ryan Kent.
Referee Serdar Gozubuyuk initially waved away Rangers’ appeals after a challenge from Slavoljub Srnic. But the Dutch referee was called to the VAR monitor and awarded the spot-kick after watching the replay.
Rangers manager Giovanni van Bronckhorst: “I’m very pleased. It was are really tough game, even with the 3-0 scoreline. It was an amazing save by Allan McGregor with the penalty.
“Red Star played a little on the edge with the offside goals, and we could see their quality, so I think we performed really well.
“John [Lundstram] had an important role. We prepared him for a different system. I think he was the key, especially in the second half.
“When I first came here I asked him to play in defence because we had no defenders and he told me ‘I’ve never played there’, but I told him with his quality he could. He is growing in his role now in the centre of midfield.”
Rangers midfielder John Lundstram: “There’s something special about being here on a Thursday night under the lights.
“The clean sheet is important. You can still see the dangers that they have. We’ve got no illusions that next week is going to be anything other than a tough game.”
Rangers captain James Tavernier: “It’s an unbelievable achievement. We are only halfway there, but the boys were brilliant.
“We really managed it well, and we’ve put ourselves in a good position. We can’t be complacent, though, and we’ll go in there like it’s 0-0. We’ve got to carry this momentum on for the rest of the season now.
“My wife gave birth to a baby daughter a couple of days ago so I had to get on the scoresheet and do the celebration.”