The 37-set run was Nadal's longest at the French Open.
Muguruza has not dropped a set so far in this year's tournament as she seeks a second championship in Paris and third major trophy overall.
Against Kerber, Halep stumbled out of the gate, dropping the first set in a tiebreaker.
Top-ranked Simona Halep has leveled at one set-all in her French Open quarterfinal against Angelique Kerber of Germany. She hurried up her strokes and easily Halep sealed the eight win in as many matches against a lefty opponent and against a top 20 player this season. Like Sharapova, Halep was erratic early, making 30 unforced errors in the first set.
"I rushed too much at the beginning", Halep told a news conference.
"I think I did a good performance today, a very serious, solid match".
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Muguruza has not dropped a set at Roland Garros and the 2016 champion needed only 70 minutes to consign a startled Sharapova to a 6-2, 6-1 defeat Wednesday.
On Court Suzanne Lenglen, Marin Cilic and Juan Martin del Potro were locked in a first-set tiebreak when play was called off.
Rafael Nadal has won 37 completed sets in a row at the French Open heading into his quarterfinal against Diego Schwartzman.
Sharapova may have vast experience on the big stage, but three double faults gifted Muguruza - who only played two games of her fourth-round clash before Lesia Tsurenko retired with an injury - a break in a nervy opening game from the Russian.
Now third in the WTA leaderboard behind Halep and Caroline Wozniacki, Muguruza will rise above them both to sit atop of the rankings with a win on Thursday. Muguruza, who won the French Open in 2016 but didn't make it out of sectionals past year, is continuing a fantastic run of tennis at Roland-Garros. She went on to commit only 16 errors over the course of the next two, which was the difference in getting the win.
She missed several chances to go 4-1 ahead but she remained able to built the points more convincingly.
She has acknowledged having trouble handling her nerves, which is part of why she was so proud about the way she overcame Kerber, a two-time major champion and former No 1. "If I do that, I will be okay after the match, no matter the result".
The No. 3-seeded Muguruza had lost all three previous meetings against Sharapova, who won two of her five Grand Slam titles at Roland Garros.