Romania's Halep was in fine form against her Red Group opponent and surged into an early 4-0 lead in the first set before progressing 6-2 6-3 in just over an hour.
She will meet Serena Williams next, with the American having also won her opening match against Ana Ivanovic.
In her maiden outing at the competition, Halep made a flying start to the contest as she reeled off the first four games with the help of two breaks of serve.
While Bouchard was able to halt her opponent's momentum - saving break point in the fifth before pulling a game back - Halep was able to tie up the remainder of the set in comprehensive fashion and move ahead in the match.
The pair had shared a win each from their two previous career meetings - both this year - but another strong start in the second sent Bouchard on her way.
The Canadian fired the first two aces of the match on her way to a 3-1 lead and, while Bouchard was able to hold serve for the remainder of the contest, Halep proved too strong.
Bouchard was left to rue her five double-faults, but Halep had some kind words for the 20-year-old.
"She is a great player, very young and she will be a great player," Halep explained, before looking ahead to her clash with Williams.
"[I will prepare] like normal I just want to enjoy the match against her. I didn't play against her this year. She is the best player in the world and I have nothing to lose."