The fourth seed demolished the Italian 6-2, 6-2 to set up an enticing clash with the Canadian hotshot, 12 years her junior, who upset former world number one Ana Ivanovic in three sets.
Chinese trailblazer Li, 31, is a two-time Melbourne finalist but has never lifted the trophy, losing to Kim Clijsters in 2011 and last year to Victoria Azarenka after dramatically twice rolling her ankle and briefly blacking out.
"I think everyone wants to win a Grand Slam. But first you have to be in the semis, right?" said Li, when asked about her chances with Serena Williams and Maria Sharapova both already out.
"But I was really happy today. At least tomorrow I have a day off. I can talk with (coach) Carlos (Rodriguez), can talk with the team and prepare for the next round."
The next match is an unknown quantity for Li with Bouchard coming from nowhere to make her first ever Grand Slam semi-final, mirroring last year's run to the last four by another teenager, America's Sloane Stephens.