Second half goals from substitute Jean-Carlos Solorzano and skipper Matt McKay cancelled out Daniel De Silva's opener but Djulbic pounced in the dying minutes to give league leading Glory a three-point buffer at the top, although second placed Melbourne Victory has two games in hand.
Brisbane, which remains in seventh spot with a game in hand over sixth-placed Melbourne City, was forced to play the final 18 minutes with 10 men after the dismissal of defender Corey Brown.
The first chance fell to Glory with German winger Dragan Paljic wriggling past a couple of challenges before bringing a smart save from keeper Michael Theo diving down to his right.
The lively Henrique wasted a glorious chance to give Brisbane a 15th minute lead when he swept his shot wide when well placed affter being set up by Thomas Broich.
Brisbane was made to pay for its wastefulness in the 26th minute when Scott Jamieson went long to Chris Harold, who headed the ball down for 17-year-old De Silva to fire home from close range.
Theo rescued the Roar from conceding a second when he kept out Andy Keogh's well struck effort in the 47th minute.
At the other end, Glory keeper Danny Vukovic got down quickly to deny McKay as the visitor sought a way back into the match.
The game turned on its head inside two minutes as Brisbane Roar struck twice to go ahead.
First, Solorzano got away from his marker Dino Djulbic to tuck his shot home from close range on the hour after Brandon Borrello had cut the ball back into his path.
Then, in the 62nd minute, McKay burst through a static defence, leaving Josh Risdon in his wake, and with Vukovic rushing off his line to meet him he swept the ball imperiously into the far corner.
Brisbane was reduced to ten men in the 75th minute when referee Ben Williams showed a straight red card to Brown after he pulled back Jamie Maclaren, even though the ball appeared to be running away from the striker as he arrowed in on goal.
Glory drew level in the 85th minute when Paljic's long range effort bounced back off the crossbar for Djulbic to slam the loose ball home.
The result left Glory without a win in its last six games.
Roar coach Frans Thijssen didn't dispute Brown's red card.
"We should have won I think because we were the better team and had much more ball possession, and even after the 2-1 lead I didn't see any problems," Thijssen said.
"But of course the red card, and it was a red card, changed things and we were left disappointed and in the last few minutes we could have lost 3-2 as well. We just had to settle for a point."
Glory boss Kenny Lowe also felt that the Glory deserved to come away with the win with some late chances for Andy Keogh and Maclaren to score the winner.
"It was probably two lost points at the death with a couple of the chances there from a yard out with Andy who couldn't sort his feet out and then Macca had one probably eight yards out," Lowe said.
"In the context there I think we missed two points."
