"I liked that when things didn't go so well, I managed to turn it around relatively quickly.
"Maybe a game or two went by but that was it, then I was able to get back to playing my game," said Bouchard.
The former Wimbledon finalist has endured a difficult couple of years, and for a period in 2018 slipped out of the top 150.
But she showed some promising signs in the second half of last year, and passed her first test today.
Brengle is a trickier proposition than she appears, as she tends to frustrate opponents and wait for errors.
That was her recipe in her biggest win to date, when she shocked Serena Williams at the 2017 ASB Classic.
On that occasion, Brengle just stayed in the fight, while Williams gradually unravelled, making a mountain of mistakes.
At times, it looked possible that Bouchard might fall into the same trap as she struggled to find her range.
Brengle constantly took the pace off the ball and there haven't been so many sliced forehands seen at Stanley Street since Miloslav Mecir and Ramesh Krishnan in the 1980s.
"You really have to create the power and the points, because she is getting a lot back and making you work for it. It was tough," said Bouchard. "Sometimes it is hard when there is so little pace."
It meant that the Canadian couldn't get into any rhythm.
But her determination to be proactive and take control of the point was obvious, even if sometimes she appeared to be trying too hard.
"Always trying to find that balance," said Bouchard. "My coach was telling me I wasn't quite being aggressive enough or finishing the point.
"She was getting a lot of balls back with some tricky slices."
While Bouchard's celebrity persona accompanies her wherever she plays, she seems focused on a positive start here in Auckland, and passed up any New Year's Eve celebrations tonight.
"I actually forgot it was New Years Eve," said Bouchard.
"People were like 'Happy New Year' and I was like 'what?' ... because I was so focused on the tournament.
"It's not a holiday, I'm working this week so definitely not doing anything exciting [tonight]."
In other matches, Monica Puig, who started a tennis revolution in Puerto Rico with her 2016 Olympic gold medal, was far too good for American wildcard Bethanie Mattek-Sands, with a convincing 6-3, 6-2 win in 74 minutes.
Other first-round winners included 2017 champion Lauren Davis, Sara Sorribes Tormo and Viktoria Kuzmova.
In the doubles, Julia Goerges and Timea Babos beat the New Zealand-Chilean combination of Erin Routliffe and Alexa Guarachi 4-6, 6-1, 10-3, while Kiwi Paige Hourigan and American Taylor Townsend beat the New Zealand combination of Valentina Ivanov and Elys Ventura 6-1, 7-5.
