Rain halted play in the first set after seventh-seeded Martic went ahead 2-0.
When play resumed, Pliskova won the next three games and broke Martic to lead 5-3 before serving out to win the first set.
Pliskova broke Martic in the second set to take a 2-1 lead and held serve before play was suspended again.
Pliskova once more came back strongly after the delay, breaking her opponent again before winning in 1 hour, 36 minutes.
Pliskova had lost to Martic in four of their previous five encounters, including a 6-3, 6-3 loss at the French Open third round.
The final had been delayed by nearly six hours after torrential rain all day.
Martic won her first title this year -- in Istanbul -- before she reached a Grand Slam quarterfinal for the first time at Roland Garros and made the top 20 rankings.
Pliskova clinched her fourth title of 2019, adding to wins in Brisbane, Rome and Eastbourne.