The Chiefs defense never seemed to get comfortable as they surrendered their second consecutive Governor's Cup at the Edward Jones Dome in St. Louis.
Tight end Lance Kendricks hauled in Bradford's first score, a 23-yard pass, less than two minutes into the game. Dann Amendola's circus catch on an eight-yard strike gave St. Louis an early 14-0 advantage.
Turnovers did the Chiefs in, as they committed four to the Rams' none.
After a lost fumble stalled the Chiefs offense on their first drive, Peyton Hillis got them on the board with a one-yard plunge early in the second quarter.
Hillis finished with five carries for 11 yards while Jamaal Charles gained 17 yards on three attempts.
Former Missouri Western kicker Greg Zuerlein booted a 52-yard field goal to push St. Louis' lead to 17-7 late in the first half. He also notched four extra points on the night.
Kansas City quarterback Matt Cassell completed 13 of 18 passes for 142 yards in his one half of play.
Ricky Stanzi, in his first game action with the second string, completed three of four for 24 yards and an interception.
Brady Quinn added a late 38-yard touchdown strike to Jeremy Horne to make it 31-17. Horne caught two balls for 43 yards while tight end Kevin Boss led the Chiefs with 62 yards.
Dwayne Bowe, who signed his franchise tender yesterday, did not play.
The Chiefs move practice to their facility in Kansas City after completing training camp in St. Joseph on Thursday.