Halep, junior champion at Roland Garros in 2008, will face Andrea Petkovic for a place in Saturday's final after the German beat former runner-up Sara Errani of Italy. (Agencies)
Russian 27th seed Kuznetsova, who won the title in 2009 to go with her 2004 U.S. Open title, took a medical timeout after the first set and came back with her left thigh strapped.
"I strained a muscle during the (last 16) match against Safarova, and then I was struggling with the pain," Kuznetsova told reporters.
"I managed to do it without a medical timeout in the Safarova match, but today it got worse," he said.
Kuznetsova wasted break points early in the second set and made too many unforced forehand errors as Halep wrapped it up on the first match point when her opponent netted a service return.
Not a hard hitter, Halep compensates for her relative lack of power with her tactical nous.
"I felt very well on court. It was a perfect day for me. I played really well. I was very aggressive. I played very fast," Halep said.
Prowling along the baseline, she moved Kuznetsova around with crosscourt shots, forcing the Russian to misfire.
She took the first game on her opponent's serve, only for Kuznetsova to break back for 2-2 as the Russian played deeper.
But Halep stuck to her strategy and won the remaining four games, taking the set when Kuznetsova sent a forehand long.
The Russian had her chance in the second game of the second set but she wasted two break points with unforced errors. She had two further chances in the fourth game, but Halep saved them with an exquisite drop shot and a superb backhand down the line to hold for 3-1.
Halep, who converted six of her eight break points while Kuznetsova blew seven of her nine chances to steal her opponent's serve, fired a few stunning return winners to break again in the fifth game.
With the contest virtually over, Halep lost focus and served three double faults in the last game, but still managed to close it down having not dropped a set in the tournament, conceding just over four games per match.
Despite that minor wobble, Halep managed to keep her composure, something she could not do in her first grand slam quarter-final appearance at the Australian Open this year when she lost 6-3 6-0 to Slovak Dominika Cibulkova.
"At that moment I didn't know how to manage the emotions before the quarter-finals," Halep, who is managed by compatriot Virginia Ruzici, the 1978 French Open champion, explained.
"I was very nervous on court and I couldn't play my game. I couldn't run the balls and I couldn't hit,” Halep said.
"Today I was very relaxed. Was a tough day because I had to wait a few hours to play because of the rain, but still it was a perfect day," Halep added.
Halep, junior champion at Roland Garros in 2008, will face Andrea Petkovic for a place in Saturday's final after the German beat former runner-up Sara Errani of Italy.