After regular playing time, the match was goalless and it went all the way to penalties.
Oskarshamn led the penalty kick 4-3 when Varberg's Keanin Ayer Boya missed his penalty.
The decisive penalty hero for Oskarshamn was 26-year-old Anton Agebjörn who has been in Oskarshamn since 2014.
Oskarshamn will thus play group games for the second season in a row.
Last year, they beat Allsvenskan Helsingborg 2-1 and went to group games.
Tonight's biggest victory was Falkenberg when they won their cup meeting with division 3 club Astrio with 9-0.
Allsvenska colleague Häcken turned 0-1 to victory with 3-1 away against the division 3 team Angered.