Williams required just 27 minutes to take the first set but was made to work hard in the second by 17th-seed Errani.
She will face Switzerland's Timea Bacsinszky who beat Alison van Uytvanck of Belgium 6-4 7-5.
Williams, French Open winner in 2002 and 2013, hit 39 winners during a dominant display.
She had dropped the opening set in the previous three rounds but set the tone for a polished performance by breaking in Errani's first service game.
A fine backhand passing shot handed Errani, 28, an immediate break back but Williams cruised to the opening set.
Errani upped her pace in the second, but it was still not enough as Williams broke for a 4-3 lead and she finished it off on her fourth match point.
Bacsinszky, 25, reached her first Grand Slam semi-final after overcoming unseeded Van Uytvanck, 21, in straight sets.
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