Then Brees added a historic accomplishment in the first quarter of New Orleans' 34-23 victory when he broke Brett Favre's NFL record by attempting the 10,170th pass of his career.
Brees, 41, already holds the NFL records for career passing yards (77,576), TD passes (549) and completions (6,885). Brady, 43, ranks second in each of those categories.
And now Brees holds a 4-3 lifetime edge against Brady in head-to-head meetings, dating to their Big Ten days in 1999.
"Of course, it's significant and it's unique, and I'd be lying to you if I said it didn't mean a little bit more," Brees said of the matchup against Brady. "I've got so much love and respect for him and what he's been able to accomplish and his journey. Really both of our journeys -- we played each other in college for God's sake, 1999. I'm sure there's some guys on the team that weren't born when that happened. We would both pinch ourselves if you told us back then we would have the opportunity to play this long and be a part of so many great teams and great moments, historic moments.
"We'll have to worry about them later in the year as well, but for now it's nice to get the win."
This was hardly the most dynamic performance by either Brees or Brady in their Hall of Fame careers. Brees completed just 18 of 30 passes for 160 yards, two touchdowns and no interceptions, and Brady was 23-of-36 for 239 yards with two TDs and two picks.
But Brees helped to cement the victory with a 46-yard deep strike to tight end Jared Cook in the fourth quarter.
Saints coach Sean Payton fell on the sword for New Orleans' offensive shortcomings, saying it was "as bad a game as I've had as a playcaller. ... It was awful."
Then Brees fell on his own sword: "Well, if you asked me how you think I played, I'd say awful as well."
"We get to be our harshest critics coming off this game," said Brees, who credited Tampa Bay defensive coordinator Todd Bowles for a plan that included a lot of zone coverages and zone pressures. "We're used to playing at a much higher level offensively -- especially in the passing game. So we'll get that back on track.
"I think the best thing we did was we took care of the football. We ran the ball well and we put together some long drives. ... Teams always have a very specific plan for us, maybe play differently than they would for other teams. We're constantly having to adjust on the fly, that's what we do. We definitely could have done a better job today with that."
Brees had originally told the Saints in February that he planned to retire, sources told ESPN's Adam Schefter. But then he changed his mind and decided to come back for a 20th season. Sources also told Schefter and ESPN's Jeff Darlington that the Saints and Brady had mutual interest in each other before Brees decided to come back.
Brees has not declared this as his final season, but he did acknowledge last week: "Hey, at this time, man, I'm on borrowed time. I've got nothing to lose. So I'm turning it loose and letting the chips fall where they may."