The 20-year-old from Malmo, the first Norwegian to qualify for figure skating in the Olympics since 1964, advanced to the free skating final after the short programme.
Norway were a figure skating superpower in the early Olympics with figure skating legend Henie winning gold three times — in 1928, 1932, and 1936.
Henie was also a ten-time world champion before finding success in Hollywood where she was one of the highest paid stars during the height of her career.
"I'm very happy that Norway has a spot here. I'm very proud to represent my country and I'm very excited," said Gjersem after taking the 24th and final qualifying spot in the short programme.
"I'm quite satisfied with my programme. It could be a little bit better, the first jump, and I could have had more speed. I could feel it in my body that I was a bit tense. I enjoyed skating and was trying to do my best."
She scored 48.56 points and it was enough to claim the final qualifying spot for Thursday's free skate final.
She became the first Norwegian figure skater to compete at the Olympic Winter Games in 50 years after qualifying at the Nebelhorn Trophy in September 2013.
Born to a Norwegian father and a Philippines mother, Gjersem wore a light blue sequined outfit as she skated to "Maria and the Violin's Sting" by Ashram.
Her twin sister Camilla Marie Gjersem is also a competitive figure skater, but watched from home.
The twins started skating in 2002, and four years later, where taken into the Sonja Henie project to prepare them for future Olympics.
In 2008-2009 she debuted in the Junior Grand Prix and Junior World Championships, and took the bronze medal in both the European Youth Olympic Festival and the Nordic Championship.
Both sisters have set their sights on the 2018 Winter Games in South Korea.
"She's (her twin) at home in Norway in the studio watching. I face-timed (on the phone) with her before my programme.
"She's always says positive things to me and she's my biggest supporter."
South Korea's Kim Yu-Na remained on course to defend her Olympic women's crown as she leads Russia's Adelina Sotnikova and Italy's Carolina Kostner by less than a point.
Kim led the 30-skater field with 74.92 as Sotnikova achieved 74.64 and Kostner 74.12.
Kim is bidding to become just the third woman to win consecutive titles after Henie, and Germany's Katarina Witt in 1984 and 1988.