By Jill Martin, CNN

(CNN) -- The dynasty lives on.

Once again, the New England Patriots are champions, grinding to win Super Bowl LIII 13-3 at Mercedes-Benz Stadium in Atlanta -- and launching Tom Brady and Bill Belichick into a different stratosphere.

They have now won six Super Bowls together, extending their record for the most by a head coach and starting quarterback combination. With the win, the Patriots are tied with the Pittsburgh Steelers for the most Super Bowl titles in NFL history.

Brady now has won more Super Bowls than any other player in history, surpassing Pro Football Hall of Famer Charles Haley (five).

"It probably won't sink in for a very, very long time," Brady said. "I'm just so blessed to play with the best teammates through the years from our '01 team and all the way through now. I love all those guys. That's what makes this special, man. It's a brotherhood. All these relationships are so important in my life, and I can't cherish it enough. It's going to be a celebration tonight."

At 41 years old, Brady also is the oldest starting quarterback to win a Super Bowl, eclipsing Peyton Manning, who was 39 when he won Super Bowl 50.

Belichick is the oldest head coach to win a Super Bowl at age 66, and no head coach has won more Super Bowls than him. Now, he joins George Halas and Curly Lambeau as the only NFL head coaches with six championships since the league began postseason play in 1933.

Belichick called this one "sweet."

"I'm proud of our football team, coaching staff, this entire organization," he said. "These guys worked so hard all year going all the way back to the offseason program in April and just grinding it out day after day. In the biggest moments when we had to play our best football and compete the hardest, they did it."

This was the pair's ninth Super Bowl appearance together, the most title games for any head coach and starting quarterback duo in NFL history.

Edelman named Super Bowl MVP

Brady was 21-for-35 passing for 262 yards, and most of those yards went to wide receiver Julian Edelman, who is boosting his hall-of-fame resume. Edelman -- who was named the game's MVP -- had 10 catches for 141 yards. In addition to already having the second-most receptions in postseason history, he's now second all time in postseason receiving yards. He trails just the legendary Jerry Rice in both categories.

Edelman, who in his college days was a quarterback at Kent State, was drafted by New England in the seventh round of the 2009 NFL draft. He is the seventh wide receiver to be named Super Bowl MVP.

"It just matters that we won, man," Edelman said. "It was a crazy year. We had a resilient bunch of guys. It was unreal, man."

After the win, among the crush of players, reporters and confetti, Brady and Edelman, who are close friends, shared a long embrace. Edelman, 32, missed all of last season with a knee injury and the first four games this season for violating the NFL's policy on performance-enhancing substances.

"He just played the best game he has all year," Brady said. "So proud of him (and) what he's accomplished coming back from his ACL (injury). He just fought it out, grinded it out just like everyone else."

High-powered offenses, but few points

The Rams had the No. 2 scoring offense in the NFL, while the Patriots were ranked fourth. But instead of a shootout, scoring came at a premium.

With 16 total points, it was the lowest-scoring game in Super Bowl history, and the Patriots' 13 points is the lowest by a winning team in a Super Bowl. It's also the first Super Bowl without a touchdown through the first three quarters.

A Stephen Gostkowski 42-yard field goal was the only scoring in the first half. The 3-0 score was the second-lowest scoring first half in Super Bowl history. Only Super Bowl IX, when the Steelers led the Minnesota Vikings 2-0, was lower.

Rams kicker Greg Zuerlein's 53-yarder tied it with 2:11 left in the third quarter.

Then came another classic Brady-led drive.

It started with a completed pass to tight end Rob Gronkowski for 18 yards. The crowd, which was majority Patriots fans, started chanting, "Brady! Brady!"

Brady then hit Edelman and Rex Burkhead for 13 and seven yards, respectively. Another throw to Gronkowski for 29 yards set up first-and-goal from the 2-yard line. Sony Michel ran it in from there for the touchdown with seven minutes to go.

The drive was five plays, 69 yards, and it took two minutes, 49 seconds, in which Brady went 4-for-4 for 67 yards.

Los Angeles tried to respond with a lengthy drive of its own, but quarterback Jared Goff was intercepted by Stephon Gilmore at the New England 4-yard line.

A 41-yard field goal by Gostkowski sealed it with 1:12 to go.

"That's my fault," Goff, in his third year at age 24, said of the interception. "I can't put us in that situation. I knew they were bringing cover-zero blitz there, and I tried to hit Brandin (Cooks) on a go-ball, and Gilmore was too far off for me to make that decision. It was a bad decision by me, and I have to do better."

McVay: 'I got out-coached'

Super Bowl LIII marked a rematch of Super Bowl XXXVI, when New England defeated the then-St. Louis Rams 20-17 on February 3, 2002. The Rams, who moved back to Los Angeles in 2016, were aiming for their second Super Bowl title and their first back out West.

Since the hiring of head coach Sean McVay, the youngest head coach in Super Bowl history at age 33, this was their second consecutive year in the playoffs.

"Coach Belichick did an outstanding job," McVay said. "There is really no other way to put it. I'm pretty numb right now, but definitely, I got out-coached. I didn't do nearly good enough for our football team. The thing that is so tough about all of this is the finality to it.

"Usually, you get a chance -- if you go through some adversity, you can bounce back right away. This one is going to stick with you and it just stings in your gut."