A win over Randers would have allowed the visitors to turn the fight for the Danish title from a two-horse-race into a three-horse-race as Brondby could have made up further ground on FC Copenhagen and FC Midtjylland.
But after the seven-goal thriller in Copenhagen a week ago, neither of the teams could break the deadlock in an uncharacteristic goalless performance in Friday's match in the Superliga.
This means that Brondby remain in third place two points after second-placed FC Midtjylland, and three points after FC Copenhagen, both of whom can extend the gap to Brondby on Sunday.
Randers is five points behind Brondby in fourth place and still have a chance in the race for third place in the league.
The first three mutual matches of the season between Randers and Brondby resulted in a total of 17 goals. And in general, the matches between the two sides have been rich on goals.
On Monday, Brondby won 4-3 in an entertaining match with plenty of chances at both ends.
But in Friday's match in Randers, chances were few and afar in a messy encounter with plenty of loss of possession, technical mistakes and lack of finely orchestrated attacks.
That was also evident from the statistics, as neither team's goalkeeper was forced to make a save in the first 45 minutes.
Yuito Suzuki came on the pitch to replace Clement Bischoff at the start of the second half, but it didn't help much for the visitors as Randers started to recover their normal stylish stride.
Randers stopper Wessel Dammers came close to finding the net after a corner kick, and full-back Oliver Olsen also tested Brondby keeper Patrick Pentz with a long-range effort. The visitors also had half chances to claim all the spoils but didn't have the quality in the decisive moments.
Randers had the opportunity for a great counter-attack in the final minutes but Brondby managed to get into position, and the generally anonymous Randers leading goalscorer Simen Nordli ran into an offside position. Thus, it all ended in a goalless draw.
Despite the loss of points, Brondby have recorded 14 out of a possible 18 points in the Superliga Championship playoffs.