TAMPA, Fla. -- In his 22nd season in the NFL, Tampa Bay Buccaneers quarterback Tom Brady is hard-pressed to find many career "firsts." But through two weeks of the regular season, Brady has thrown a league-leading nine touchdown passes, besting his previous career high, after throwing five scores in a 48-25 victory over the Atlanta Falcons Sunday.

"I think any time you have a guy like Tom leading us, I think you're in a good spot," said wide receiver Chris Godwin, who has two touchdowns in two weeks. "All the skill players around him trust him, and trust is one of the biggest things you can have in this game."

Brady tossed a pair of touchdowns each to tight end Rob Gronkowski and wide receiver Mike Evans, and connected with Godwin in the fourth quarter. Defensive back Mike Edwards finished the job with two fourth-quarter pick-sixes, becoming the first player since Robert Massey in 2012 to record two interceptions returned for scores in the fourth quarter of a single game, and the first player since Zach Brown with two such touchdowns in a single game.

Including the postseason last year, the Buccaneers (2-0) have now scored at least 30 points and won each of their past nine games, the longest streak in NFL history. Brady and Gronkowski have also combined for six touchdowns in three games dating back to Super Bowl LV -- their best three-game mark in 11 seasons together. And Gronkowski joined Ben Coates (1994) and Dee Mackey (1962) as the only tight ends in league history with at least two touchdown receptions in each of their team's first two games.

"It's dope. I think the more we go, the more we figure out each other, I think the better it's gonna be," Godwin said. "It's not easy to put up 30 points in this league. I think that's a testament to not only our offense, but our defense continuing to give us opportunities to go out there and score touchdowns.

In addition to Edwards' two scores from the defensive side -- just the third time in Buccaneers franchise history that a player has achieved that feat -- outside linebacker Shaquil Barrett picked off Matt Ryan in the third quarter, setting up Evans' second touchdown.

"What I think, and I'm sure other guys feel the same way, is I think we can do better. I really do," said Brady, who has thrown for 655 yards this season. "And I really think we have the opportunity, with the way that the games are flowing and the opportunities we're getting with the ball -- we have even more. ..."

"We're trying to do something special with the offense this year," said Evans, who had five catches for 75 yards. "We did pretty good today making plays, but obviously there's still more out there. ... But it's cool, man. Everybody has to be ready. We have so many guys that can get the ball at any given time. We just have to make sure we're ready."

Despite the potent scoring, the Buccaneers' offense still feels like it hasn't reached its full potential. Its five turnovers through two games are tied for the most in the NFL through Sunday's 4 p.m. ET games, as well as tied for the league lead of 22 penalties.

The Buccaneers have also posted a 39.1% conversion rate on third down, tied for 17th in the league. Scoring touchdowns in the red zone has been their strength, with their seven touchdowns in that area tied with the Arizona Cardinals for most in the NFL.

"We've been a little loose with the ball," said Brady, who lost a fumble on a first-quarter sack. "Some penalties at different times that have knocked us out of some scoring drives, some missed throws that I've had, some missed reads. I certainly wish I had made some better throws tonight. But it's good to get the win, be 2-0 and there's a lot to build on, and it's good to beat a division opponent."

The Buccaneers meet another high-powered offense in Week 3 on the road in the Los Angeles Rams, who are averaging 30.5 points a game with new quarterback Matthew Stafford. That will give an indication of where the Bucs stand this early in the season, especially after a 27-24 loss to the Rams at home in Week 11 last year.

"Obviously we got 14 points out of the defense but we left points out there offensively," coach Bruce Arians said. "I haven't seen us get close to playing consistently yet. Hopefully we'll get there next week because we are going to have to."