The exhibition opener marked the NFL coaching debut of Chip Kelly, who left the University of Oregon to take the Philadelphia job following the departure of Andy Reid.
Brady completed 7-of-8 passes for 65 yards and a touchdown, that coming on a 13-yard throw to Shane Vereen in the second quarter.
Stephen Gostkowski put the Patriots in front for good at 17-14 with a field goal of 34 yards in the second quarter and Blount scored on a 51-yard run to make it 24-14 at the half.
Blount, whose first three seasons in the NFL were spent with Tampa Bay, added a 1-yard touchdown in the third quarter. He finished with 101 yards on 11 carries.