Romania's Halep is the highest seed remaining in the women's tournament, and her victory over 2009 champion Kuznetsova sets up a last-four meeting with Germany's Andrea Petkovic, who defeated Sara Errani by the same scoreline earlier in the day.
Neither Halep nor Petkovic have contested a Grand Slam final before, but the duo will go head-to-head for the right to do so on Thursday.
After rain had delayed the start of the match on Court Suzanne Lenglen, Halep made her intentions clear early on as she claimed the opening two games to open up a 2-0 lead.
Kuznetsova hit back with a break of her own to level matters at 2-2, but that proved to be her last game victory of the opening set as Halep asserted her dominance.
Rapturous applause greeted a rare ray of sunshine on the French clay, and the two players shared the first two games of the second set following a brief medical time-out for the Russian as she had treatment on her left thigh.
However, Kuznetsova was left playing catch-up after losing her next two service games.
She looked capable of a comeback when she won to love on Halep's serve to pull herself back to 4-2, but defeat in the next meant the tie was all but over.
Halep was far from elegant in serving for the match, and had to survive two break points before eventually booking her place in the semi-finals.