De Minaur has experienced a dream week in his home city and dominated the opening set of the final on Saturday, but 21-year-old Russian Medvedev battled back to triumph 1-6, 6-4, 7-5.
That ranking is soon set to rise to No.127 as he embarks on an Australian Open campaign starting against Tomas Berdych.
"I'm the kind of person, the more emotions I feel, the less I show them, actually, especially if they are good ones", Medvedev said.
"I played well and I'm looking forward to doing well in Melbourne".
The longer the rallies the more risky de Minaur became and he claimed the opening set after winning six games on the trot.
But Medvedev lifted in the second set, cleaning up his unforced errors and pushing de Minaur to 3-3 before breaking the Australian's serve amid several tense, long rallies, including one totalling 31 shots.
By the match's half-hour mark, de Minaur had already broken Medvedev three times and converted his third set point, much to the delight of the packed crowd at Ken Rosewall Arena.
The comeback was on and he refused to surrender, breaking to level at 5-5, before Medvedev returned the favour and served it out to love to claim his first ATP title.
The gritty Spaniard raced through the first set and then proved just the stronger in the decider to win 6-1 4-6 7-5. Medvedev certainly has the firepower to trouble De Minaur but the young Aussie has shown a willingness to knuckle down and fight against opponents who are not as tenacious on court.
"I'm tremendously proud. I put in all the hard yards, and it's great to see the results coming through".