Quarterback Sam Darnold threw two interceptions for Seattle but regrouped to make two touchdown passes, the second to star receiver Jaxon Smith-Njigba in overtime, before adding the two-point conversion to clinch victory.
The Rams led 13-7 at half-time before Kenneth Walker III burst through to run in a 55-yard touchdown for Seattle.
Rams cornerback Josh Wallace then returned Darnold's first interception for 56 yards and Blake Corum barged in from a yard on the next play.
Rams quarterback Matthew Stafford found Puka Nacua for a touchdown early in the fourth quarter to make it 30-14, but Rashid Shaheed gave Seattle hope by scoring with a 58-yard punt return.
Darnold then found AJ Barner in the end zone and Seattle added the two-point conversion to take the game to overtime.
Although Nacua then raced in for his second touchdown, Smith-Njigba replied to set up the game-winning score and finish with 96 receiving yards.
The 23-year-old leads the NFL with 1,541 receiving yards for the season, with Nacua second (1,367) after claiming 225 yards from 12 receptions on Thursday.