Wilder's performance of "Don't Worry" and Bengtsson's "Constellation Prize" were voted through by viewers.
Neither artist is a stranger to the world of song competitions. In 2008, Bengtsson placed third in Sweden's Idol competition and Wilder's debut came in 2014's Melodifestivalen where she earned second place overall.
Two other songs will get another shot at making it to the final after securing a place in the competition's so-called second chance round. They are Albin and Mattias Andréasson with the song "Rik" and Samir and Viktor with their song "Bada nakna".
Melodifestivalen continues with its second round of eliminations on February 13 in Malmö. The final round will be held in Stockholm on March 12.