The world number one sprained her ankle in her first round match at Melbourne Park on Tuesday but showed no sign of restricted movement in a 65-minute romp on Margaret Court Arena.
Marching around the court like she meant nothing but business, Halep's confidence appeared to increase as she grew into the match and she broke Bouchard seven of the eight times the Canadian served.
"I felt the pain but I didn't think about it," Halep said. "I couldn't practice much but during the match I just forgot about it. I had a very tight tape. I could move.
"The most important thing is that I could play my game not thinking about the ankle. I did it great today."
Bouchard beat Halep in the 2014 Wimbledon semi-finals, the same year she reached the last four at Melbourne Park, but is now ranked a lowly 112th in the world.
She broke the Romanian at the start of both sets and had her moments in what was at times a hard-fought contest but it was her inability to hold her own serve that put paid to her hopes of advancing.
Her faulty forehand did not help her cause and contributed greatly to a tally of 26 unforced errors, the last of which brought defeat after Halep had fired down a huge forehand which she could only balloon wide.
Halep moves on to a third round encounter with American world number 76 Lauren Davies, happy to have avoided the early exits that befell her on her last two visits to Melbourne and with her tenuous grip on the number one ranking still holding.
Rather than concern her, the 26-year-old said the injury would actually allow her to play with more freedom.
"For sure I'm not 100 percent," she said. "But I don't feel pressure. I feel a little bit more relaxed because I have nothing to lose.
"I'm just trying to stay focused on my game, nothing else. Definitely to be careful with the movement on the court, not forcing anything. I'm just going out there and feeling the ball."
(Reporting by Nick Mulvenney in Sydney, editing by Amlan Chakraborty and Pritha Sarkar)
