The Rams (8-3) won for the fifth time in six outings as the Saints (8-3) had their eight-game winning streak snapped.
Goff, who did not throw a touchdown pass in last week's loss to the Minnesota Vikings, clicked with veteran Sammy Watkins and rookie Josh Reynolds. Greg Zuerlein added four field goals, three from at least 46 yards, as the Rams prevailed.
New Orleans, which averaged 30.2 points during its winning streak, was stifled by the Rams' defense, which sacked Brees three times. The Saints, who were 3-for-13 on third downs, entered the game averaging 415 yards but were held to 346.
Brees, who directs the NFL's second-best passing offense, was 22 of 32 for 246 yards and a score. Much of Brees' production came late against the Rams' soft coverage as they protected their lead.
Goff, who lost to the Saints last year in his rookie season, completed 28-of-43 attempts for 354 yards. He was intercepted for the first time since Oct. 22 when Watkins dropped a ball into P.J. Williams' hands.
Copper Kupp paced all receivers with 116 yards on eight receptions.
Rookie Alvin Kamara, who had a combined 188 yards, hauled in a 15-yard touchdown pass from Brees with less than two minutes remaining.
Zuerlein's final field goal came from 26 yards with 2:30 to play.
The Saints settled for Wil Lutz's 21-yard field goal to get within 23-13 with 10 minutes remaining. Brees' touchdown pass to Mark Ingram II was erased on tight end Michael Hoomanawanui's pass interference penalty.
Zuerlein's 49-yard field goal to start the fourth quarter pushed the Rams ahead, 23-10.
Lutz's 50-yard-field goal in the half's closing minutes shaved the Rams' lead to 17-10.
Goff heaved his second scoring pass, a 7-yarder to Reynolds, giving the Rams a 17-7 advantage. It was Reynolds' first touchdown catch, second reception of the season, and it was set up by Kupp's 53-yard reception.
Kamara ripped off a 74-yard, first-quarter touchdown run that pulled the Saints to within 10-7. Kamara went right, cut left, then headed back right where he hugged the sideline until cutting up-field when Mark Barron made a last-ditch effort to tackle him.
Zuerlein kicked a 50-yard field goal in the opening quarter, pushing the Rams ahead 10-0.
The Rams struck fast, capping their opening possession on Watkins' 5-yard scoring catch for a 7-0 lead.
NOTES: New Orleans CB Marshon Lattimore (ankle) didn't play. ... CBs Dexter McDougle and Sterling Moore were added to the Saints' roster. ... Rams WR Robert Brooks (shoulder), the team's leading receiver, was out. Los Angeles LB Mark Barron (arm) left in the third quarter and didn't return. .... The Rams signed CB Kevin Peterson to the roster. ... Hall of Fame G Tom Mack lit the Coliseum's Olympic torch before the game.