The 19-year-old from Lille, ranked 132nd in the world, took one hour and 44 minutes to dispatch Boserup, 25, to reach Sunday's title match.
Dodin, who had never played in a WTA quarter-final until this week, will next face the winner of a later semi-final between two qualifiers, 104th-ranked American Lauren Davis and 233rd-ranked Czech Tereza Martincova.
None of the remaining players have ever won a WTA crown.
Boserup, ranked 125th, had not reached a WTA semi-final since 2014.