Big-hitting Mensik sent down 18 aces to win 6-3, 7-6 (7) and secure a second career title following victory at last year's Miami Open.
The 20-year-old, the youngest player with a ranking in the world's top 25, showed he could be a threat at the year's first major at Melbourne Park, where he is seeded 16.
The tall European had too many weapons for his 39th-ranked Argentine opponent, mixing an aggressive serve with deft touches at the net.
Mensik broke once in each set and needed a fightback to win the tiebreak, saving three set points on the way.
He said he was thrilled with his serving game.
"After pre-season, obviously you're not in rhythm and you're coming for a season with a lot of energy," Mensik said in a court-side interview.
"So I'm super happy that I showed a performance that I wanted.
"Seb is a great fighter and it's super-difficult to hit a winner against him.
"I was able to stay focused and keep the spirit to the end."
The tournament proved demanding for both players, who had to play their quarter-finals and semi-finals on Friday because of rain delays.
Baez, who has won six of his seven titles on clay, knocked out top-seeded American Ben Shelton in the quarter-finals.
It was the first loss this year for the 25-year-old, who won all three matches at last week's United Cup, including an upset of American world number nine Taylor Fritz.