Instead, it was Alexander Zverev, defeated in Saturday's singles by de Minaur, who went on to seal the tournament-winning points for Yannick Noah's European squad by defeating American Learner Tien in the key singles on Sunday afternoon (Monday AEST).
Agassi adores de Minaur's never-say-die competitiveness and had paired him with American Taylor Fritz in the final day's critical opening doubles, trusting they could down Italy's Flavio Cobolli and Czech Jakub Mensik, thus overturning Europe's overnight two-point lead.
The plan, if they won, was for de Minaur to also then tackle the unenviable clash with Europe's other major spearhead Carlos Alcaraz later on the final evening.
Instead, Agassi's plans all went awry as de Minaur and Fritz were outplayed 7-5 6-3 which only extended the home team's lead.
That meant Zverev could then get to the 13-point mark that would guarantee Europe regaining the trophy they'd lost in San Francisco last year as he faced American Tien.
World No.2 Zverev, who's had an epic year in which he's won his first two grand slams at Roland Garros and Flushing Meadows, then duly sealed Europe's record-extending sixth Laver Cup title with a 7-6 (7-3) 6-3 victory that took their unassailable advantage to 13-5.
The tie over, that meant de Minaur was spared having to later duel with the Spanish great Alcaraz, who he's yet to beat in six meetings.
It was a frustrating end to the tournament for 'Demon', who'd taken his unbeaten individual singles record to 4-0 after earning the victory from match point-down against Zverev.
Now in his third appearance at a Laver Cup, he was experiencing the first taste of Team World being defeated after he'd helped them prevail in 2022 at the same O2 Arena in London as well as last year in California.
"We were very close," de Minaur said. "Yesterday, we won two supers [10-point tiebreakers] and lost one with Taylor playing an epic match.
"We were up against it from the get-go; we were the underdogs and put in a hell of a fight. A couple points here and there could have changed the whole tie."
It was the fourth time Zverev had helped to clinch the Cup for Europe, having secured the winning points in Chicago in 2018, Geneva in 2019, and in Boston in 2021.
His win sparked jubilant celebrations, with the European players leaping in celebration and even enjoying a sing-song on court.
"I'm happy that I did it today," Zverev said. "But massive credit to the entire Team World. They pushed us all the way.
"I think we had a great team, great team chemistry and a great team effort. We're definitely happy that we won!"
"We had three chances to close it out in the singles. Especially with Carlos playing after me, I think that gives me a lot of confidence and gives me a little bit of freedom to play.
"I think Carlos is also very happy that I closed it out. And me too, by the way! I'm very happy that I won."
