The Australian, who is moving into the top 10 in the world rankings, cruised to a 6-3 6-3 victory against a below-par Kontaveit in their semi-final.
Barty has won three WTA Tour titles, but the decider in Miami – against either Simona Halep or Karolina Pliskova – will be her first at WTA Premier Mandatory level.
She capitalised on what was a rusty display from Kontaveit, who committed 33 unforced errors to lose in one hour, 17 minutes.
Rain interrupted the clash early, but there were no further delays after play resumed at 2-2 in the first set.
A Kontaveit double fault and forehand into the net gave Barty a 4-3 lead before the 12th seed took the opener 6-3.
Kontaveit, the 21st seed, finished with 17 unforced errors in a difficult first set.
It seemed a lengthy third game in the second set would prove important as Kontaveit broke for 2-1, but the Estonian was lacking patience as she gave up that lead.
Barty won five consecutive games from 3-1 down, sealing what was an impressive victory with an ace.