The Chinese number one struggled on her serve to beat America's Cohen 6-3 6-4 in one hour and 34 minutes on a hard outdoor court.
Li will face eighth seed Bojana Jovanovski of Serbia in the next round of the south coast city's inaugural tournament, which has been designed as a warm-up event for the Australian Open.
Second seed Marion Bartoli booked a quarter-final meeting with Klara Zakopalova of the Czech Republic by eliminating Switzerland's Stefanie Voegele 7-5 6-4.
France's Bartoli racked up nine double faults against the 22-year-old qualifier but fought hard to guarantee her place in the last eight alongside Zakopalova, who beat Ukraine's Elina Svitolina yesterday.
Earlier in the day, Chinese world number 177 Zhou Yi-Miao moved beyond Chang Kai-chen of Taiwan with a 4-6 6-2 7-6 (7/3) victory. Zhou will face Laura Robson's conqueror, Monica Niculescu of Romania, in the next round.
China's Shuai Peng and Annika Beck of Germany complete the quarter-final line-up, after posting second-round wins on New Year's Day.