Wentz connected with wide receiver Mack Hollins for 64 yards, threw a 4-yard strike to tight end Zach Ertz and a 9-yard pass to undrafted free agent running back Corey Clement. Wentz's fourth score came on a 10-yard pass to wide receiver Nelson Agholor for a 31-17 lead with 11:10 remaining.
Wentz has already thrown 17 touchdown passes through seven games, one more than he had all of last season. He finished the night 17 of 25 for 268 yards with one interception.
The Eagles (6-1) won their fifth straight. The Redskins (3-3) dropped into a second-place tie in the NFC East with the Dallas Cowboys.
Philadelphia came right back and extended its lead to two touchdowns.
The news wasn't all good for the Eagles, however, as left tackle Jason Peters was carted off the field with a leg injury with 14:06 remaining in the third quarter.
Philadelphia was leading 17-10 when Peters got tangled up with defensive lineman Ziggy Hood. Peters' leg appeared to bend awkwardly, and the veteran had an air cast placed on it before heading out on a cart.
Peters, a nine-time Pro Bowl tackle, didn't return.
Rookie kicker Jake Elliott's 42-yard field goal with 6:19 left gave the Eagles a 34-17 lead.
Cousins' third touchdown pass, his second to Reed, this one for 12 yards, cut the deficit to 34-24 with 3:17 left.
Cousins completed 30 of 40 passes for 303 yards with one interception.
The Redskins drove 66 yards on eight plays on their first possession but settled for a 27-yard field goal from Nick Rose for an early 3-0 lead.
Following some sloppy play through the first quarter, the Eagles put together a solid drive and it resulted in a 50-yard field goal from Elliott with 13:15 remaining in the second to tie the game at 3.
It was Elliott's 11th consecutive field goal and his fourth from 50 yards or longer this season.
Washington responded quickly and capped a seven-play, 81-yard drive with a 7-yard touchdown pass from Cousins to running back Chris Thompson for a 10-3 advantage with 9:14 left in the first half. Eagles linebacker Najee Goode got turned around, allowing Thompson to walk into the end zone untouched.
Wentz struggled mightily through most of the first half, going 3 of 8 for 30 yards and three sacks. But Wentz showed some toughness and lofted a beautiful 64-yard touchdown pass to rookie wide receiver Hollins to tie the game at 10 with 3:19 remaining.
With 22 seconds left in the half, Wentz continued his improved play and tossed his second touchdown pass, this time a 4-yard strike to Ertz for a 17-10 lead.
NOTES: Redskins QB Kirk Cousins announced on Twitter that his grandmother, Jean Cousins, died Sunday night. ... The Eagles played without CB Ronald Darby (ankle) and LB Mychal Kendricks (hamstring). ... Redskins CB Josh Norman sat out a second consecutive game with a fractured rib. ... Former Eagles K David Akers was inducted into the team's Hall of Fame in a halftime ceremony. ... K Nick Rose played in his first career game for the Redskins. ... Eagles LB Jordan Hicks had been questionable with an ankle injury but was able to start. However, he was injured on the second play of the game and had to be helped off the field.