The Romanian third seed played some neat and tidy tennis in the opening set, lost the plot in the second and then wrapped up the victory to set up a second-round meeting with Magda Linette of Poland.
Halep seized control with an early break and tightened her grip in a one-sided first set, containing her opponent's power.
But Tomljanovic started to hit the ball harder and by the time Halep had started to figure out how to deal with her pace the Australian had taken the second set.
Experience, however, prevailed in the decider as Halep won six of the seven remaining games.
"It was not easy because of the emotions, the pressure," Halep told reporters. "But these are nice emotions and I am happy I could win the match and get to play another one."
It was the first time Halep stepped back onto Court Philippe Chatrier for a competitive match since she lifted the Suzanne Lenglen Cup a year ago, and she felt at home even if the stadium has been revamped.
"Maybe the sound is a bit different but the size of the court is the same," she explained.
Halep indeed seemed comfortable on the red clay and she said the only pressure she would put on herself had nothing to do with results.
"It's the first time in this position, but it's a nice feeling so I can't complain, it's nice to be in this position. I have expectations for myself but I'm not going to put pressure on myself for the result," Halep added.
"I feel different since I won the French Open. Everything is a bonus and I see tennis differently, my life differently.
"My main goal is to see how good I can be this year and maybe for a few more years, we will see."
(Reporting by Julien Pretot; Editing by Ken Ferris and Toby Davis)
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