While Rodgers claimed his second victory over Brady in five meetings, the anticipated offensive battle was ultimately superseded by a defensive struggle.
Reigning back-to-back NFL MVP Rodgers threw two touchdowns in the first half but the Packers were shut out in the second, while Tampa Bay left it until the dying stages to finally score a touchdown.
Seven-time Super Bowl winner Brady led an 89-yard drive that ended with him finding Russell Gage in the endzone with 14 seconds left to make it a two-point game.
But the Buccaneers were unsuccessful with the two-point conversion as they fell to their first loss of the season.
Super Bowl favourites the Buffalo Bills fell to their first defeat of the campaign as they were beaten 21-19 by division rivals the Miami Dolphins.
Buffalo's loss came despite a monster effort from Allen, who threw for 400 yards and two touchdowns on 63 passing attempts.
But when they got the ball back with just over 90 seconds left after a Miami punt in their endzone resulted in a safety, the Dolphins defence stood tall as they improved their record to 3-0.
The Philadelphia Eagles are also 3-0 after they cruised past NFC East rivals Washington Commanders 24-8, with quarterback Jalen Hurts throwing for 340 yards and three touchdowns.
The Kansas City Chiefs suffered their first defeat of the season in a 20-17 loss to the Indianapolis Colts.
Indianapolis quarterback Matt Ryan orchestrated the comeback victory with a 16-play, 76-yard drive that ended with a game-winning touchdown pass to Jelani Woods.
Baker Mayfield also got his first win in a new uniform, leading the Carolina Panthers to a 22-14 success against the New Orleans Saints.
Last season's AFC champions the Cincinnati Bengals got their first win of the new campaign by beating the New York Jets 27-12.
The Denver Broncos eclipsed the San Francisco 49ers in a dour 11-10 victory in Sunday's late game, while the Los Angeles Rams beat the Arizona Cardinals 20-12.
Lamar Jackson threw four touchdowns and rushed for another as the Baltimore Ravens beat the New England Patriots 37-26 while the Minnesota Vikings battled back in the fourth quarter to beat the Detroit Lions 28-24.
The Chicago Bears beat the Houston Texans 23-20, despite two interceptions from quarterback Justin Fields, while the Jacksonville Jaguars eased to a 38-10 victory over the injury-hit Los Angeles Chargers.
The Atlanta Falcons got their first victory of the campaign by winning 27-23 at the Seattle Seahawks, but the Las Vegas Raiders are 0-3 after a 24-22 loss to the Tennessee Titans.