Andreeva, who turned 19 on Wednesday, will face Marta Kostyuk after the Ukrainian beat Anastasia Potapova 6-2 1-6 6-1 in the second semi-final.
"I feel so much adrenaline inside, I feel like I'm still nervous," Andreeva said in the post-match interview.
"Honestly, I'm just so happy that I won ... I'm very happy with how I served today."
Baptiste had shocked world No.1 Aryna Sabalenka in the quarter-finals, but the 24-year-old struggled as ninth seed Andreeva conceded only two points on serve in the first set.
The American stood firm until the seventh game, when her forehand landed wide, giving Andreeva a break point. The former French Open semi-finalist sent a perfect backhand down the line to earn the decisive break that sealed the set.
Baptiste, who made 16 unforced errors in the first set, continued to struggle in the second, handing Andreeva a break for a 3-2 lead.
But the American fended off a match point in the ninth game before Andreeva, serving for the set, double faulted and botched a smash before Baptiste landed two perfect winners to get her first break of the match, making it 5-5.
The second set reached a tiebreak and a newly confident Baptiste won four points straight before Andreeva fought back with precise backhands near the sidelines and saved three set points.
Baptiste fired down an ace to save a match point but hit a return long as Andreeva clinched victory, reaching the final of a WTA 1000 tournament for the third time after winning the Dubai Championships and the Indian Wells Open last year.
Kostyuk battled past lucky loser Potapova in a scrappy night session marked by poor serving and frequent errors from both players.
The 26th seed took the opener with two breaks, but the second set swung the other way as Potapova raced through it in under 30 minutes. Kostyuk then surged to a 4-0 lead in the decider before closing it out, helped by Potapova's sixth double fault.
Kostyuk, who did not shake hands with her Russian-born opponent who now represents Austria, advanced to her first WTA 1000 final where she will aim to replicate her victory over Andreeva from their only previous meeting in Brisbane in January.
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