Brown connected on kicks of 40, 44, 33, 46 and 27 yards while Eli Manning went 25-of-39 through the air for 246 yards with no interceptions as the Giants (2-6) won a second straight following six consecutive losses starting the season.
On defense, the Giants forced three Eagles turnovers and allowed just 201 total yards.
Philadelphia's Michael Vick returned after a two-game injury absence but lasted less than a half after aggravating a previous hamstring pull.
Rookie Matt Barkley took over with the Eagles trailing 12-0 but finished with just 158 passing yards on 17-of-26 efficiency while tossing an interception and losing a fumble.
LeSean McCoy managed 48 rushing yards on 15 carries for Philadelphia (3-5).