Brady broke out of a tie with now-retired Peyton Manning for number one on the all-time wins list.
"We're in the locker room with a walking legend," Patriots cornerback Malcom Butler said after Brady threw for one touchdown pass in the victory that took the Patriots to 10-2 for the season.
He broke out of a tie with now-retired Peyton Manning for number one on the all-time wins list, including regular-season and post-season contests.
"He has the most wins in quarterback history in the NFL, but he still comes to work like he hasn't accomplished anything," Butler added of Brady -- who might have passed the milestone sooner but for his four-game Deflategate suspension to start this season.
The record put Brady in the spotlight, but the Pats defense also came up big, holding the Rams to 25 yards of offense in the first half -- the fewest yards ever allowed by New England in a half.
It was the kind of performance New England needed as they adjust to life without star tight end Rob Gronkowski, who will miss the rest of the season after back surgery this week.
LeGarrette Blount, who turns 30 on Monday, romped 43 yards for a touchdown on a fourth-and-1 on New England's first possession.
Brady hit Chris Hogan with a 14-yard TD pass in the second quarter and Stephen Gostkowski kicked four field goals.
Three of Gostkowski's field goals were from 45 yards or more -- a welcome sign that he has broken out of the slump that has seen him miss four field goals and three extra-points this season.
"It's a start, it's one game," Gostkowski said. "Every week is a different challenge."
Kansas City safety Eric Berry, riding on the emotion of his return to his hometown of Atlanta, produced a spectacular display that included a game-winning interception return in the Chiefs' 29-28 victory over the Falcons.
Berry, who beat Hodgkin's lymphoma, had a 37-yard interception return for a touchdown in the first half, then picked off an attempted conversion pass in the fourth quarter and raced 99 yards for what proved the deciding two points.
"The last time I came home during the season it was to get chemotherapy," said Berry, who handed his touchdown ball to his mother in the stands.
"This time it was to play a game, so I was thankful for the opportunity. I take pride in a lot of things people take for granted. I cherish everything that comes my way."
The Dallas Cowboys -- who notched their 11th straight win on Thursday -- officially became the first team to clinch a playoff berth when NFC East rivals Washington dropped a 31-23 decision to Arizona.
In Oakland, Derek Carr threw for 260 yards and two touchdowns as the Raiders roared back with 29 unanswered points to beat the Buffalo Bills 38-24.
The Raiders won their sixth straight and improved to 10-2 -- their best start since 2000.
Baltimore Ravens quarterback Joe Flacco had a big day, throwing for 381 yards and four touchdowns in a 38-6 blowout win over Miami that snapped the Dolphins' six-game winning streak.
The Chicago Bears blew out the San Francisco 49ers 26-6 at snowy Soldier Field. Niners quarterback Colin Kaepernick was sacked five times and completed just one pass for four yards was benched in the fourth quarter in favor of Blaine Gabbert, but that didn't stop San Francisco from falling to an 11th straight defeat.