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.
Scottish Premiership leaders Rangers are back in league action on Sunday with a short trip to face St Mirren (12:00 BST).