Li, the No. 4 seed this year, defeated No. 28 Flavia Pennetta 6-2, 6-2 and Bouchard followed with a 7-5, 5-7, 6-2 win over 14th-seeded Ana Ivanovic. Li first advanced to the Australian Open semifinals in 2010 and lost in the finals in Melbourne in 2011 and 2013. Bouchard had never before made it past the third round of a major tournament.
Bouchard had beaten Ivanovic before -- winning at last year's Wimbledon Championship in the second round -- and didn't seem cowed by the big stage. She had seven breaks versus Ivanovic, with two coming in the final set. Bouchard didn't allow Ivanovic a break opportunity in the third set.
The only trouble Li had in her 67-minute win over Pennetta was one dropped service game. She still took 73 percent of the points on serve and 54 percent off Pennetta's serve while finishing off five of her eight break chances.
Li and Bouchard have played once before, with Li taking a 6-4, 6-4 decision in a 2012 match in Bouchard's hometown of Montreal.
The other semifinal will be set Wednesday when two-time defending champion Victoria Azarenka, the No. 2 seed, plays fifth-seeded Agnieszka Radwanska and No. 11 Simona Halep goes against Dominika Cibulkova.
Halep is looking for her first Grand Slam semifinal berth while Cibulkova, who played in the semis at the 2009 French Open, is seeking a second.
Radwanska, in her fourth consecutive quarterfinal at Melbourne, has twice before made a major tournament semifinal, getting that far in the last two Wimbledon Championships. Azarenka is a seven-time Grand Slam semifinalist, with all of those appearances coming since Wimbledon in 2011.
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