The Patriots suddenly find themselves within a touchdown and an extra point (important since each kicker has missed one) from taking their first lead.
The Eagles, who have punted only once, drove 51 yards in eight plays but had to settle for a 42-yard Jake Elliott field goal.
Marquis Flowers tackled Nelson Agholor for an 8-yard loss on third-and-three from the New England 16.
Philadelphia leads 32-26 with 14:09 remaining.