In a ruthless performance on Rod Laver Arena, a steely-eyed Barty raced through the straight-sets victory in just 54 minutes to continue her perfect start to the year.
Australia's world No.1 opened the season with singles and doubles glory in Adelaide and stamped her Open favouritism once more on Monday night.
"It's certainly nice to be back on home soil and playing as well as I did tonight. It was a lot of fun out here," Barty said.
"I felt like it was nice and clean. End-to-end I did a good job in adjusting.
"There is quite a bit of wind at court level here so I thought I did a good job and some tough service games from down that end.
"Overall I felt like I was able to find my forehands, control the court with my forehand.
"Tonight it was just nice and solid to get out here and play a decent match and feel like I enjoyed it."
The top seed also played Tsurenko in the first round at Melbourne Park in 2020.
On that occasion, Barty had to fight back from a set down to reach the second round.
But there were few moments of resistance from Tsurenko this time around as an imperious Barty took just 24 minutes to claim the first set, dropping only 12 points.
Barty staved off an early attack from Tsurenko, comfortably saving two break points when leading 2-0, then kicked into another gear to seize the upper hand.
The top seed was similarly dominant in the second set, racing through the first five games.
Barty spurned two match points on Tsurenko's serve that could have earned her first-round double-bagel wins at the Open two years in a round.
But the Wimbledon champion made no mistake on her own serve, closing out victory in less than an hour.
Barty will play Lucia Bronzetti on Wednesday after the Italian qualifier beat Russia's Varvara Gracheva 3-6 6-2 6-3.