The Australian's power game overwhelmed the Romanian for the second straight year at Roland Garros, this year's victory coming in 66 minutes.
Stosur thought the imposing manner of her victory showed how much she had matured on the court.
"Getting off to that good start and being mentally tough and picking up the game as the match went on is really encouraging," she said.
She will play world number 51 Gisela Dulko in the next round, the Australian holding a 2-0 edge in their head-to-head including a victory last month on clay in Madrid.
"It is a good match-up for me, we played a three-setter in Madrid which I was able to get through and we both know each others games quite well," she said.
"I have to go out and still play aggressively and she can play very well and be tricky."
Fellow Australian Anastasia Rodionova joined Stosur in the second round with a 6-1, 6-4 victory over unheralded Edina Gallovits-Hall.
It is the second year in a row that Rodionova has reached the last 32 in Paris.
Rodionova won the match in 71 minutes and will next play the winner of third seed Vera Zvonareva and German qualifier Sabine Lisicki.
Rodionova upset Zvonareva in the second round at Roland Garros last year, before the Russian went on to reach the final of Wimbledon and the US Open.
Queenslander Stosur was shifted off centre court for the first time in five matches at Roland Garros on Wednesday morning.
With the likes of world No.1 Caroline Wozniaki and Roger Federer opening proceedings on the two main showcourts, the Australian was pushed onto court 1.
She instantly made herself comfortable, racing through the first set in just 26 minutes.
Stosur's game cooled off momentarily early in the second set with some wayward shots.
But no sooner could Halep enjoy the fact she was on the board than Stosur had broken back and seized control of the match.
Despite the occasional lapse, Stosur's performance demonstrated she is going to be tough to beat again this year.
The high bounce she is producing off the clay from her heavy top-spin tends to neutralise all but her tallest opponents.
There is talk among the players that the new Babolat balls used in Paris are producing even more bounce on the red dirt than normal, which plays into the Australian's hands.
Stosur has said she has noticed very little difference with the balls, but she is sponsored by Babolat and had the benefit of receiving a box of them the week before the grand slam.
-AAPTags: sport, tennis, australia, france First posted May 25, 2011 21:40:00