Culpepper, who completed four of eight passes for 47 yards, drove the Raiders 73 yards in nine plays late in the first period. He ended the drive by hitting Ronald Curry for 19 yards.
Jordan scored on a 1-yard run in the final minute of the first half to give the Raiders a 17-3 advantage at intermission.
The Rams' lone touchdown came with two minutes left in the fourth quarter when Gus Frerotte hit Marques Hagans from six yards out.
Josh McCown started at quarterback for the Raiders and completed six of nine passes for 138 yards.
St. Louis quarterback Marc Bulger was eight of 21 for 109 yards.