Brady threw touchdowns to Rob Gronkowski and Mike Evans as his side led 31-0 at one stage.
The reigning NFL champions made light work of the challenge ahead of them, running out 31-15 winners in the wildcard round.
Two unanswered touchdowns on short runs from first Giovani Bernard and then Ke’Shawn Vaughn had the Bucs well ahead, leading 17-0 at half-time before Brady took centre stage.
The 44-year-old has seven Super Bowl rings in his collection and will be aiming to fill yet another finger having passed for two touchdowns in the third quarter to secure the win.
The Eagles hit back late on through running backs Boston Scott and Kenneth Gainwell but they never threatened to spring a shock comeback on the dominant Bucs.