First-half goals from Leon Balogun and Kemar Roofe were enough to give Steven Gerrard's side the points and move them off the bottom of Group A.
Balogun opened his account for the club with a thumping 18th-minute header from James Tavernier's corner.
Roofe put the game beyond the reigning Danish Superliga champions on the half-hour mark with his 25th goal in 49 appearances.
Both sides were searching for their first goals in Group A, having drawn blanks in their opening two fixtures.
Rangers broke their duck early on – and so did Balogun, with the centre-half netting his maiden goal for the club in his 40th appearance.
The visitors spurned a great opportunity to equalise when Andrija Pavlovic fired over from close range, and they were made to pay as the hosts doubled their lead through Roofe's tap-in after half an hour.
Reacting quickest after Alfredo Morelos' header was saved, the former Leeds United striker was initially denied by the offside flag, but that decision was correctly overturned following a consultation with VAR.
Brondby squandered another great chance within seconds of the second half beginning when Uhre shot wide after Borna Barisic's loose pass inadvertently sent him clear on goal.
That was the closest the visitors came to threatening a comeback and inflicting a fourth defeat in five home European matches for Rangers.
Scott Arfield and Fashion Sakala went close to adding a third later on for Gerrard's team, who saw out victory and claimed a hugely important three points.