Pliskova and Romanian Halep played a tight first set, which Pliskova eventually clinched with some outstanding court coverage as she used her long reach to chase down a series of shots by Halep that would have been winners against many a player.
Suitably buoyed, Pliskova raced through the second set and was on the brink of victory, up 5-0 when another shower sent the players to the locker room as the clock struck midnight.
They eventually returned an hour later for Pliskova to close it out in a near-empty arena.
Earlier, Barty was forced to wait out an hour-long rain delay before her match and when it started she and 21st seed Kontaveit were only on the court for about five minutes before weather halted play again.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
They returned about two-and-a-half hours later to play one more game and then headed back to the locker room for a third rain delay, this time for two hours.
Barty finally secured the win with an ace on her second match point, six-and-a-half hours after the original scheduled start.
"I have been here for 12 hours today, but really happy with the way I was able to come out after the rain delays and kind of get on the front foot pretty early," said Barty, 22, who has three career titles.
"I did the best with what I had and was able to get out of some tight service games at crucial times and get a bit of a roll on."
(Reporting by Andrew Both in Cary, North Carolina and Frank Pingue in Toronto; Editing by Ian Ransom/Sudipto Ganguly)
