Marshall Faulk added 85 yards rushing and a score as the Rams (11-3) increased their winning streak at the Edwards Jones Dome to 13 games and moved ahead of Philadelphia (10-3) in the race for home-field advantage throughout the NFC playoffs.
The Eagles play at Miami on Monday night.
The Seahawks (8-6) lost their sixth straight road game and are battling for a wild-card spot.
Faulk scored on a five-yard run and Bulger hit Isaac Bruce with an 18-yard touchdown in the first quarter to stake the Rams to a 14-2 lead.
The Seahawks fought back and closed within 24-22 on a two-yard touchdown run by Shaun Alexander with 10:18 left in the fourth quarter.
Faulk rushed for 51 of his yards on the Rams' last drive, setting up a 46-yard field goal by Jeff Wilkins with 1:37 remaining.
Swim Week Miami Beach 2014 [PHOTOS]