Josh Reynolds and Gerald Everett snagged touchdown passes from Goff in the final clash of week seven between two franchises with rich NFL histories.
"It was a dominant performance. It was lights out for us today," said defensive tackle Aaron Donald of the Rams, who improved to 5-2 on the season.
The Rams have been reliant on their defence this season, especially Donald, who now has four career sacks against the Bears.
"I was just trying to fly around make plays, and disrupt," said Donald, who combined with a teammate to get to Bears quarterback Nick Foles.
The Rams' defence held the Bears to 49 rushing yards while recording four sacks and two interceptions.
Quarterback Goff was 23 of 33 for 219 yards and Malcolm Brown ran for 57 yards for the Rams, who are 3-0 at their new state-of-the art, $5 billion stadium in south central Los Angeles.
Bears QB Foles was 28 of 40 for 261 yards. Chicago's only touchdown came on an eight-yard fumble recovery and return in the fourth quarter by safety Eddie Jackson.
"We take it one game at a time," said Rams coach Sean McVay. "We got to continue to play well in all three phases. It was a big win against a tough opponent for sure."