Glenn on course for Olympic berth at US Figure Skating championships
Glenn, who is bidding to make the US team for next month's Milan-Cortina Winter Olympics after missing out on Beijing four years ago, produced a near flawless performance to score a national record 83.05 points.
The 26-year-old two-time US champion leads world champion Liu, on 81.11, with Isabeau Levito in third.
Glenn is now targeting victory when the women return for Friday's free skate.
Glenn said her performance had been inspired by the memory of her grandmother Barbara, who passed away in February last year.
"For some reason I just felt my grandma with me today, and that meant a lot," Glenn said. "I think she really got me through this."
In the pairs short program, Alisa Efimova and Misha Mitrofanov produced a dazzling display to score 75.31 points and take a healthy lead over Audrey Shin and Balazs Nagy on 67.67.
While Efimova and Mitrofanov look poised to retain their US crown, the duo are sweating on their eligibility for a place at the Olympics.
The Finland-born Efimova, who has also skated for Russia and Germany in the past, married US citizen Mitrofanov two years ago but has not yet received a US passport and as things stand is not eligible to compete at the Olympics.
"To be honest, it’s out of our control," Mitrofanov said on Wednesday.
"So for us, we don't focus on that. We focus on what we can control, which is our skating. And that's what we're really proud of today."
The pairs free program is on Friday.