Match ends, Rangers 2, Brøndby IF 0.
Rangers produced one of their most complete performances of the season, says manager Steven Gerrard, by easing Brondby aside at Ibrox to revive their Europa League knockout hopes.
Leon Balogun's header and a Kemar Roofe tap-in - from a parried Alfredo Morelos header - gave Gerrard's side their first points at the third attempt to lift them off the bottom of Group A.
Morelos, seeking his 100th Rangers goal, and substitute Scott Arfield both hit woodwork as the hosts were denied more goals to cement their superiority.
Lyon's comeback win at Sparta Prague leaves Rangers a point behind the Czechs and six adrift of the French at the halfway stage of the group.
And a trip to Denmark next will hold no fears for the Scottish champions after Brondby offered feeble opposition in Glasgow.
"It is certainly up there if you look at the performance over the 90 minutes," said Gerrard.
"We deserved the victory, we played with a lot of control and style, we could have maybe got another couple of goals.
"We have played really well for 45 minutes or 60 minutes but for some reason consistently we haven't found that level where we are churning out 90 after 90 minutes so that is the most pleasing thing for me tonight."
Morelos' scoring record this season - five goals in 15 games - was highlighted pre-match by Gerrard as below the standard he expects from his strikers.
After defeats to Lyon and Sparta the visit of the ailing Danish champions - Brondby are floundering in sixth place in their domestic league - provided the ideal chance for the forward and Rangers to rediscover a cutting edge.
The Colombian 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 foiled 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 clinically shown the way with his first Rangers goal. James Tavernier - under a hail of missiles raining down from Brondby fans - swung in an inch-perfect 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 spot on 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 Croat 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 to fire wide.
Aribo was rightly aggrieved not to 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 tweaking 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 did they say?
Rangers manager Steven Gerrard told BT Sport: "The players delivered the gameplan we set out. You can pick the bones out little moments but in the main we controlled, we dominated. It's really close to the 90-minute performance we've been looking for.
"We've kick-started our Europa League campaign. We've got to replicate this performance and result in a couple weeks' time. If we do it's going to be very interesting. We've given ourselves a good chance. If we get out this group it'll be a superb job."
Scottish Premiership leaders Rangers are back in league action on Sunday with a short trip to face St Mirren (12:00 BST).
What the stats say
- Rangers have won eight of their nine matches against Danish sides in all European competitions (D1), winning at least once against each of the five sides they have faced from Denmark.
- Rangers came into this match off the back of three consecutive Europa League defeats and were winless in four in the competition. Their two goals tonight were more than they had netted in their previous four matches in the competition (1).
- Brondby remain the only side without a goal in this season's Europa League campaign, despite registering 16 attempts on goal.
- Leon Balogun's opener was his first ever goal for Rangers and his first in any club competition since netting for Brighton against Crystal Palace in the Premier League back in December 2018.
- Twelve of Keemar Roofe's 13 goals for Rangers in 2021 have come at Ibrox (the other away at St Johnstone in September).
- Since Steven Gerrard's first game in charge of Rangers in July 2018, James Tavernier has provided 48 assists across all competitions, at least 20 more than any other player for the club during this period.
- 26BalogunSubstituted forBasseyat 64'minutes
- 4LundstramBooked at 29minsSubstituted forArfieldat 78'minutes
- 7HagiSubstituted forWrightat 78'minutes
- 20MorelosSubstituted forSakalaat 71'minutes
- 25RoofeSubstituted forBacunaat 78'minutes
- 23CappisSubstituted forGreveat 81'minutes
- 19FrendrupBooked at 41minsSubstituted forBørkeeietat 73'minutes
- 25Ben SlimaneSubstituted forRadosevicat 45'minutes
- 14MensahSubstituted forRiverosat 62'minutes
- 11UhreSubstituted forHedlundat 63'minutes
- 31Singh Sidhu
- Fran Jovic
- Shots on Target
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.