Brady, 42, completed 28 of 42 passes for 348 yards, three scores and an interception in the win Sunday at FedEx Field in Landover, Md. The six-time Super Bowl champion now has 71,923 career passing yards, trailing only Drew Brees and Peyton Manning.
Brady passed Favre for third place on the all-time list in the third quarter of Sunday's win. The future Hall of Famer found Julian Edelman on an 11-yard pass to move past the longtime Green Bay Packers gunslinger.
"I consider all those team awards," Brady said during his weekly interview Monday on WEEI. "I have the privilege of playing with so many great players over the years, and representing our team and our coaches, and Mr. Kraft and his family. It's been a privilege for me.
"I could never have imagined playing 20 years in the NFL. I could never have imagined everything that has happened over the course of my career. I've looked up to Brett. I've looked up to Peyton. There has been some really spectacular players who have played in the NFL. Again, I just love doing what I love doing. I love playing football. Hopefully I can keep it going, too."
The Redskins (0-5) took a 7-0 lead over the Patriots (5-0) with a Steven Sims 65-yard rushing score in the first quarter. Brady hit Edelman for a 6-yard score on the Patriots' next drive, but kicker Mike Nugent missed the extra point and New England still trailed heading into the second quarter.
Nugent hit a 37-yard field goal on the Patriots' next drive for a 9-7 advantage and New England never looked back. The Patriots kicker converted for a third time before the half to extend the lead to five points.
Brady hit Brandon Bolden on a 29-yard touchdown toss on the opening drive of the second half. Sony Michel scored on a 14-yard run to give the Patriots a 26-7 lead with 4:42 remaining in the third quarter. Brady threw his third and final touchdown toss to Ryan Izzo with about nine minutes left in the game.
Michel ran for 91 yards and a touchdown in the win. Edelman pulled in eight catches for 110 yards and a score. Colt McCoy completed 18 of 27 passes for 119 yards and an interception for the Redskins. The Patriots sacked McCoy six times and held the Redskins to 220 total yards. Jamie Collins had three tackles, a sack, a forced fumble and a fumble recovery in the victory.
The Patriots host the New York Giants at 8:20 p.m. EDT Thursday at Gillette Stadium in Foxborough, Mass. The Redskins -- who fired coach Jay Gruden Monday morning -- face the Miami Dolphins at 1 p.m. EDT Sunday in Miami.
"We've had really major problems coming out of halftime, and contrary to beliefs, it's not about second half adjustments as much as it's about second half mentality," Gruden told reporters Sunday. "For whatever reason, we have gotten beaten up in the third and fourth quarter. Penalties, turnovers, lack of third down play-making that killed us."
Brady trails Manning by just 17 yards on the all-time passing yards list. He is 2,922 yards behind Brees, who is currently out due to a thumb injury. Brees passed Manning for first on the all-time list in October 2018.