The 31-year-old, who has reached two of the last three finals at Melbourne Park, blasted the 28th-seeded Flavia Pennetta off the court with a 6-2 6-2 win with a strong first serve and barrage of powerful ground strokes.
That 66-minute performance, however, had its roots in a third round clash with Lucie Safarova, when the Czech ran the fourth seed all around the court and held a match point before Li scraped to a 1-6 7-6 (2) 6-3 victory in two hours, 27 minutes.
"He didn't tell me what I should do. He just asked me 'what do you want? Why you do this?'" Li said of what Rodriguez had said to her after the Safarova clash.
"After three questions, I was feeling he was already punching me down already. So I was like, 'okay, I should do something'.
"So that's why I start next day to prepare (for the rest of the tournament). I try to do what I say, because before I always promising, I will try to do, I will try to do, but I never do.
"I think this is why (my play) turn around."
One of the harder hitters on tour, Li's groundstrokes were sublime on Tuesday as she painted the tramlines and controlled the pace of the match from the baseline.
Pennetta, who had been impressive in her victory over ninth-seed Angelique Kerber in the fourth round, was unable to get into the match with her service game falling apart.
Her lack of accuracy, with less than 40 per cent of her first serves going in, allowed Li to jump out to a 5-0 lead in the first set and 4-0 in the second. She won just 25 of 54 points on her own serve in the entire match.
"Was really tough today because I didn't serve really well," Pennetta said.
"My serve doesn't work in the way I would like to."
"She made no mistakes at all in the first five games, maybe one or two, and a lot of winners.
"I was trying to push, but she was faster and stronger than me today ... she was too good."
Li's performances at Melbourne Park since 2010 have been impressive - she has made the semi-finals four times and the final twice.
Her only exit before the final four in that period was a fourth-round loss to Kim Clijsters in 2012 and her path to this year's final has been opened up by Serena Williams' loss in the fourth round to Ana Ivanovic.
Li, who will now face Eugenie Bouchard after the Canadian rising star beat 14th seed Ana Ivanovic 5-7 7-5 6-2, said she had not even thought about facing Williams - or any other potential opponent.
"When I think about that, I always lose next day," she said.
"So for me I'm just 'okay, because she's not my next opponent ... you just follow what you should do'.
"I always do well here. I wish I could do one more step this year."
30-Eugenie Bouchard (Canada) beat 14-Ana Ivanovic (Serbia) 5-7 7-5 6-2
4-Li Na (China) beat 28-Flavia Pennetta (Italy) 6-2 6-2
- Sports & Recreation
- Flavia Pennetta
- Lucie Safarova