The Seahawks looked to start positively on fourth and one but saw Russell Wilson sacked on the 36-yard line.
It didn't take long for last season's Super Bowl finalists to break the deadlock, however, with rookie wide receiver Tyler Lockett announcing himself by touching down with a 57-yard punt return and Steven Hauschka converting the kick.
Into the second quarter, and the Rams returned the favour early on when Tavon Austin ran the ball into the endzone from 16 yards, while Zuerlein levelled things with the extra point.
A 33-yard kick from Zuerlein then put the Rams ahead for the first time with 7:31 left on the clock in the second quarter.
The hosts looked certain to have the half-time lead, but Hauschka kicked again in the last second from 25 yards to level things at the break.
Into the third, and a second field goal from Hauschka gave the Seahawks a narrow advantage, but those points were sucker-punched minutes later when Rams quarterback Nick Foles ran the ball into the endzone from the one-yard line.
The Rams went on the offensive again with 4:30 on the clock in the third quarter when Austin, scorer of the hosts' first, ran an incredible 75-yard punt return touchdown to put Jeff Fisher's side 24-13 up.
The visitors were not finished, though, and Wilson fed Jimmy Graham in the endzone early on in the fourth quarter, with Marshawn Lynch bursting over for a two-point conversion to put the Seahawks within three points of their rivals.
Fourth-quarter domination continued for Seattle with a third field goal of the day from Hauschka, before Cary Williams scooped a fumble to run the ball into the endzone and make it 31-24 to the visitors with less than five minutes left.
The game looked to be over, but Foles found Rams tight end Lance Kendricks in the Seahawks endzone one minute from the finish before Zuerlein converted the extra point to send the game into overtime.
It was Zuerlein who had the last laugh, too, when he drove a field goal between the posts from 37 yards out for a three-point advantage and opening day victory.