Bautista Agut made it mission accomplished for Spain by defeating Poland's world No.9 7-6 (8-6) 2-6 7-6 (7-5) at Ken Rosewall Arena.
Spain was beaten by Serbia in the final two years ago, but will get another opportunity to lift the trophy on Sunday when it faces Canada or Russia.
Bautista Agut has won all four matches he has played in the competitions this week and came out on top despite Hurkacz hitting 61 winners to his 28.
The 33-year-old only made 14 unforced errors and secured the only mini-break in a final-set tie-break to put Spain into the final once again.
He said: "It's a match that I will always remember. I think both of us could get the win today. He also really deserved a lot of good things. But this is our game, this is tennis.
"Today I was the one who got the win. I think I also deserved it. I did a lot of good things on the court."