Rookie running back Cam Akers had 171 yards on 29 carries in the 24-3 win on Monday at SoFi Stadium in Inglewood, Calif.
The Rams defense had six sacks and held the Patriots to 220 total yards.
"We were out-coached, outplayed, about everything, really," Patriots coach Bill Belichick told reporters. "They did a good job in all the areas.
"We weren't good enough to really be able to stay with them. They're a good football team that played well. They played and coached better than we did and deserve to win. We just have to all do a better job, starting with me, but it just wasn't our night."
The Rams began the night with a six-play, 70-yard touchdown drive. Quarterback Jared Goff ended the possession with a one-yard rushing touchdown. Matt Gay made a 35-yard field goal on the Rams' next drive for a 10-0 lead.
Patriots quarterback Cam Newton threw a pick-six on the first play of the second quarter that was returned for 79 yards by Rams linebacker Kenny Young.
Patriots kicker Nick Folk made a 29-yard field goal with 1:08 remaining in the first half to make the score 17-3 at the break.
The Rams offense came out hot again in the second half. After the Los Angeles defense forced a punt on the Patriots' first possession of the third quarter, Goff orchestrated a 16-play, 88-yard drive, which took 9:42 off the clock.
Goff ended that possession with a two-yard touchdown toss to Cooper Kupp for the final points of the game.
The Rams quarterback completed 16 of 25 passes for 137 yards, a touchdown and an interception, in addition to his rushing score.
Young had six tackles and a sack, in addition to his interception for the Rams. Los Angeles defensive end Michael Brockers had two sacks and defensive tackle Aaron Donald had 1.5 sacks in the victory.
Newton completed 9 of 16 passes for 119 yards and an interception before he was benched in the second half.
The game was the first matchup between the teams since Belichick and the Patriots beat coach Sean McVay's Rams in Super Bowl LIII almost two years ago.
"We have a lot of respect for them, but it's a totally different year," McVay said. "It doesn't have anything to do with what it occurred a couple of years ago.
"It's a big win for us to get our ninth win, get a couple days of rest, and then really see if we can finish up this last quarter of the season strong. I like the position that we're in but we have a long way to go."
The Patriots (6-7) travel next to face Dolphins at 1 p.m. EST on Sunday at Miami's Hard Rock Stadium and the Rams (9-4) host the New York Jets at 4:05 p.m. EST.