In contrast to her topsy-turvy two previous matches, which both went to three sets, the 2011 French Open champion took just 55 minutes to get past her fourth round opponent.
In reaching the last eight, Li has matched her Wimbledon best, having made the quarter-finals in 2006 and 2010.
The 31-year-old will face either Polish fourth seed Agnieszka Radwanska or Bulgarian world number 72 Tsvetana Pironkova on Tuesday for a place in the semi-finals.
Li hit 26 winners to Vinci's eight, and her serving was far more reliable than the Italian's on the 2,000-seater Court 3.
Making the last 16 matched her previous Wimbledon best, achieved last year.
However, the 30-year-old has never beaten Li in all their four encounters, dating back to 2001.
Li's run to the Australian Open final earlier this year was the only other time she has made a Grand Slam quarter-final in nine majors since winning the French Open two years ago.
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