United needed an injury-time goal to dump two-time champions Melbourne Victory out of the playoffs campaign with defender Dino Djulbic landing the knockout blow.
Despite the game being decided so late, Bleiberg was delighted with the performance of his side who will now meet Adelaide United in the next phase.
“It was a terrific performance and to win it so late made it very dramatic,” said Bleiberg after the game.
“Both sets of players were brave in the way they went about their work in such hot conditions, but fortunately it was our day today.
“In the second half we made Melbourne look like a tired team and overall I felt we deserved our win.”
The 1-0 win overturned a 2-0 loss to the Victory at the end of January and kept the Gold Coast, who finished fourth on the regular season table, in the hunt for a title in just their second season.