The Romanian club destroyed the visitors in the first leg, 75-57, giving them an 18-point aggregate lead heading into next week's second leg in Russia.
Shay Doron, Tina Thompson and Linda Fröhlich all had big games for Targoviste.
Doron and Thompson scored 15 points apiece with the latter also pulling down 10 rebounds.
Fröhlich and Olena Ogorodnikova each finished with 14 points, with the former a rebound shy of a double-double.
Targoviste only led 19-16 by the end of the first quarter but they began the second frame with an 11-0 run that was sparked by a Fröhlich jump shot.
Doron capped the spurt with a lay-up as the Targoviste team took control for good.
The lead ballooned to 45-29 by half-time and they stayed in front by double digits the rest of the way.
Kursk got 16 points and seven rebounds from Jillian Robbins while Varvara Psareva scored nine and grabbed 10 boards.