The energetic 19-year-old had been bossing his older and more experienced opponent on Margaret Court Arena, and with a vocal Australian crowd behind him, the match result looked beyond doubt.
But to Laaksonen's credit he emerged a different player in the third set. With the finish line in sight for de Minaur, Laaksonen, 26, began taking more risks and they began paying off. He upped his ground stroke speed, worked the court harder and started to find cheap service points. He was no longer playing as his ranking suggested; world No. 166.
It wasn't long before the match was tied at two sets apiece. Laaksonen had wrestled control of the momentum while de Minaur started to look fatigued. For the first time in the match, the young Australian wasn't the favourite to progress.
However, while others may have stumbled or simply given in, de Minaur raised the stakes again, found a second wind and delivered one of the more memorable performances we've seen from an Australian male in recent times.
'The Demon,' as he is nicknamed, snared the early break in the fifth set to go up 2-0 and from there he was able to keep Lakksonen at bay. Throughout the final set he won eight more points and made seven less unforced errors, eventually taking it 6-3 in a match time of three hours and 52 minutes.
There were shades of Lleyton Hewitt's grit and determination in his performance - it was perhaps unsurprising that the Australian Davis Cup captain was cheering him on and riding every shot from his players' box. After all, Hewitt was the master of the Melbourne Park five-setter.
"That was definitely pretty special. I would like to thank everybody that stayed out, the support was amazing as always," a humble de Minaur said post-match over raucous applause. "You guys got me through that and I can't thank you guys enough.
"I didn't want to lose. I had to make sure I composed myself and mentally reset for the last set, try not to get down on myself and be positive.
"I could do this every single day of the year. There's nothing better than playing in front of you guys whether it's one hour, two hours, five or 10. I just love it and I can't wait to get back out here and play in front of you guys again."
It's been a whirlwind 12 months for de Minaur. He has gone from little known fighter to Australia's highest ranked men's singles player, overtaking the inconsistent Nick Kyrgios and temperamental Bernard Tomic in the process.
Just days before the Australian Open got underway, de Minaur was hoisting his first piece of silverware after defeating Italian journeyman Andres Seppi for the Sydney International title.
De Minaur, the 27th seed at this year's tournament, will now face world No. 2 and 2009 Australian Open champion Rafael Nadal in the third round.
The pair also met in the same stage at Wimbledon last year and it was the 17-time Grand Slam champion who put on a clinic to dispatch the Aussie 6-1, 6-2, 6-4, but de Minaur says things may not be so straightforward for Nadal this time around.
"I feel like I learnt a lot from that experience. I'm really looking forward to just having fun, going out there and competing," de Minaur said. "I've already stepped out on court and played him, so that whole experience of playing Rafa, that's not new to me anymore.
"Hopefully this time around I can go in a bit more relaxed, just focus on myself and try to play some good tennis."
One thing is certain for de Minaur, win, lose or draw, he'll be a fan favourite at Melbourne Park for years to come.