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Alfredo Morelos was kept waiting for his 100th Rangers goal as Steven Gerrard's men revived their Europa League knockout hopes by easing to victory over Brondby at Ibrox.
Leon Balogun's thumping header and a Kemar Roofe tap-in - from a parried Morelos header - gave Rangers their first points at the third attempt to lift them off the bottom of Group A.
Morelos hit the post and substitute Scott Arfield struck the crossbar as the hosts were denied further goals to cement their superiority.
Lyon's comeback win at Sparta Prague leaves Gerrard's side a point behind the Czechs at the halfway stage of the group.
A trip to Denmark next will hold no fears for the Scottish champions after Brondby offered feeble opposition in Glasgow.
Morelos' scoring record this season - five goals in 15 games - was highlighted pre-match by manager Gerrard as below the standard he expects from his strikers.
The visit of the ailing Danish champions - Brondby are floundering in sixth place in their domestic league - provided the ideal chance for Morelos and Rangers to rediscover a cutting edge.
However, the Colombian's search for his landmark goal will continue into a third game after he endured a night of frustration.
Morelos had already tested Thomas Mikkelsen with a 20-yard strike when he left the goalkeeper helpless with a whipped effort on the cusp of half-time only to be denied by the upright.
Mikkelsen denied Morelos again midway through the second period, with the 25-year-old glumly trudging off moments later to be replaced by Fashion Sakala.
Centre-back Balogun had shown the way with his first Rangers goal paving the way for victory. James Tavernier - under a hail of missiles raining down from Brondby fans - swung in a corner and Balogun outmuscled Morten Frendrup to power a header past Mikkelsen.
Brondby ought to have been level when Andrija Pavlovic slashed a near-post effort wide, and their profligacy was soon punished.
Joe Aribo's delivery was perfect for Morelos but the striker headed straight at Mikkelsen, whose parry was knocked home by Roofe. The offside flag was immediately raised to mute home fans' celebrations, before Croatia referee Fran Jovic awarded the goal following a VAR check.
With a two-goal cushion and half an hour played, Rangers looked home and dry. Brondby's only threat came from Rangers lapses, with Borna Barisic's awful backpass sending Mikael Uhre clear. But with just Allan McGregor to beat, the striker fired wide.
Aribo was rightly aggrieved not be given a penalty when the midfielder's darting run was halted by Sigurd Rosted.
And goalscorer Balogun's night ended prematurely when he made way for Calvin Bassey after appearing to tweak a hamstring.
Rangers ought to have added to their lead in the closing stages but Arfield swept the ball against the bar from a Scott Wright cutback and Sakala was denied one-on-one by Mikkelsen.
Man of the match - Joe Aribo
What did we learn?
Rangers are still not firing on all cylinders, but this was a professional performance and a hugely important win as they bid to reach the knockout phase for the third season running.
And while form continues to elude Morelos, Roofe is proving a reliable source of goals, with the Jamaica international taking his club tally to eight in 14 matches this season.
At the other end, Rangers' biggest danger was complacency as they gave Brondby a couple of chances that better sides would have profited from.
What's next?
Scottish Premiership leaders Rangers are back in league action on Sunday with a short trip to face St Mirren (12:00 BST).
Line-ups
Rangers
Formation 4-3-3
- 1McGregor
- 2Tavernier
- 6Goldson
- 26BalogunSubstituted forBasseyat 64'minutes
- 31Barisic
- 17Aribo
- 4LundstramBooked at 29minsSubstituted forArfieldat 78'minutes
- 10Davis
- 7HagiSubstituted forWrightat 78'minutes
- 20MorelosSubstituted forSakalaat 71'minutes
- 25RoofeSubstituted forBacunaat 78'minutes
Substitutes
- 3Bassey
- 16Patterson
- 22Bacuna
- 23Wright
- 27Kelly
- 28McCrorie
- 30Sakala
- 33McLaughlin
- 37Arfield
Brøndby IF
Formation 3-5-2
- 16Mikkelsen
- 3Heggheim
- 5Maxsø
- 4Rosted
- 2Gammelby
- 23CappisSubstituted forGreveat 81'minutes
- 19FrendrupBooked at 41minsSubstituted forBørkeeietat 73'minutes
- 25Ben SlimaneSubstituted forRadosevicat 45'minutes
- 14MensahSubstituted forRiverosat 63'minutes
- 11UhreSubstituted forHedlundat 63'minutes
- 9Pavlovic
Substitutes
- 8Greve
- 15Riveros
- 17Bruus
- 18Tshiembe
- 20Fallenius
- 22Radosevic
- 24Divkovic
- 27Hedlund
- 29Bjur
- 31Singh Sidhu
- 40Ægidius
- 42Børkeeiet
Live Text
Match ends, Rangers 2, Brøndby IF 0.
Second Half ends, Rangers 2, Brøndby IF 0.
Attempt saved. Joe Aribo (Rangers) left footed shot from outside the box is saved in the bottom left corner. Assisted by Steven Davis.
Fashion Sakala (Rangers) wins a free kick on the left wing.
Foul by Jens Gammelby (Brøndby IF).
Attempt saved. James Tavernier (Rangers) right footed shot from outside the box is saved in the bottom right corner. Assisted by Scott Arfield.
Foul by Scott Wright (Rangers).
Andreas Maxsø (Brøndby IF) wins a free kick in the defensive half.
Scott Arfield (Rangers) wins a free kick in the attacking half.
Foul by Sigurd Rosted (Brøndby IF).
Attempt saved. Fashion Sakala (Rangers) left footed shot from the centre of the box is saved in the centre of the goal. Assisted by Calvin Bassey.
Substitution, Brøndby IF. Mathias Greve replaces Christian Cappis.
Scott Arfield (Rangers) hits the bar with a right footed shot from the centre of the box. Assisted by Scott Wright.
Substitution, Rangers. Scott Wright replaces Ianis Hagi.
Substitution, Rangers. Juninho Bacuna replaces Kemar Roofe.
Substitution, Rangers. Scott Arfield replaces John Lundstram.
Foul by Kemar Roofe (Rangers).
Blás Riveros (Brøndby IF) wins a free kick on the left wing.
Substitution, Brøndby IF. Tobias Børkeeiet replaces Morten Frendrup.
Substitution, Rangers. Fashion Sakala replaces Alfredo Morelos.