A quick toilet break helped Nishikori reset as he built a double break, with the insurance coming in handy when broken serving for the title at 5-1.
Breaking Medvedev for a 3-1 lead in the third set, Nishikori held firm to seal the match in a little more than two hours for his first trophy since winning in Memphis in February 2016.
Tsonga - a 2008 Australian Open finalist - wound back the clock to beat de Minaur 6-4 7-6 (7-2) on Pat Rafter Arena as he continued his promising return following a seven-month injury hiatus a year ago.
Tsonga said he knew he had to attack during the tiebreak.
That became 6-4 before Medvedev won the next four points to claim the set.
Five solid holds later they went into a tie break where Alex moved 2-1 up with a smash victor before losing two points on serve that cost him dearly. "Tomorrow I will go for a trophy", Nishikori, the 2014 United States open finalist said after the win.
At 4-4 in the decider, Medvedev then rallied from 0-40 down to gain the decisive break when his former world No. 3 opponent hit a cross-court forehand well wide.
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"I'm really happy that finally I've won this title, it's been like seven or eight times at this tournament".
Medvedev rose to No. 16 in the rankings after winning three ATP titles previous year, including the Sydney International before being a second-round casualty in Melbourne.
"Great final today, I lost to him (Medvedev) a year ago in the final in Japan, so I'm happy to get revenge today". "I mean top players, champions of our sport", Medvedev said.
"Rennae said 'I am absolutely sure you can win this match, ' which gave me some confidence and belief that I can do it".
"To see that what I have been working on in the off-season works here in Brisbane is already is a good sign".