PHILADELPHIA -- The Philadelphia Eagles had lost four games going into Sunday's match-up against the Atlanta Falcons and they had a chance to win all four in the fourth quarter. Finally, the Eagles came through in the clutch.

"It's good to get the monkey off our back," quarterback Carson Wentz said after the Eagles beat the Falcons 24-15 at Lincoln Financial Field. "It's huge. Finally, in the fourth quarter we finished the ball game. We're going to build on this, for sure."

The Eagles trailed 15-13 when running back Ryan Mathews scored on a 5-yard run for the winning points with 6:49 left in the game, and then their defense kept the high-flying Falcons offense in check, holding them to just 43 yards on their final four possessions. The Eagles wrapped it up when Caleb Sturgis drilled a 48-yard field goal with 1:57 left to make it a two-score game.

"I tip my hat to Philadelphia," Falcons coach Dan Quinn said. "They outplayed us in all three areas -- offense, defense and special teams. We had the lead and when it was time to close it, we were not able to do it."

Mathews, who had lost his starting job to Darren Sproles, rushed for a season-high 109 yards on 19 carries and rookie Wendell Smallwood had 70 yards on 13 carries. As a team, the Eagles rushed for 208 yards, which is the most the Falcons had given up all season. The previous best against them came in Week 2, when Oakland rushed for 155 yards.

"Everyone knows that when you can run the ball like we did today it just opens up everything you do on offense," Eagles tackle Jason Peters said. "We got it rolling early and that really set the tone of the game."

Wentz completed 25 of 36 passes for 231 yards, with no touchdowns or interceptions. Atlanta quarterback Matt Ryan completed 18 of 33 for 267 yards, with a touchdown and an interception on the Falcons' final possession of the game.

The Eagles (5-4) got off to a great start as they drove 81 yards in 12 plays on their first possession of the game to take a 7-0 lead on running back Mathews' 4-yard touchdown run. Mathews carried the ball on the final five plays of the drive and averaged almost 7 yards per carry.

After Sturgis missed a 44-yard field-goal attempt, the Falcons (6-4) drove downfield -- highlighted by a 29-yard pass to Julio Jones -- and scored their first points on Matt Bryant's 38-yarder, which made it 7-3 with 9:36 left in the second quarter. Then Atlanta tacked on another three points before the half, as Bryant kicked a 43-yarder to make it 7-6 with 2:59 left in the first half.

"We kicked too many field goals," Falcons center Alex Mack said. "When you're playing a good team on the road you have to capitalize on your opportunities and that means seven points instead of three. We didn't do that today, and that's a big reason we lost a game we could have won."

The Eagles also scored after a long drive to open the second half, but this time they had to settle for a field goal after a holding penalty on center Jason Kelce on first-and-10 from the 12. Sturgis' 29-yarder made it 10-6 with 8:16 left in the third period. But the Falcons answered with another field goal of their own -- this time from 46 yards -- which made the score Eagles 10, Matt Bryant 9.

The NFL's top scoring offense finally came to life to give the Falcons their first lead of the game. On second down from the Atlanta 24, wide receiver Taylor Gabriel put a move on defender Leodis McKelvin and sprinted past him. Gabriel was all alone when he cradled Ryan's pass and he cruised the final 45 yards to give Atlanta a 15-13 lead after Bryant missed the point-after kick.

Then it was the Eagles offense's turn to push the ball into the end zone, helped along by a 21-yard pass-interference penalty against Falcons cornerback Brian Poole, which put the ball on the Atlanta 5. On the next play, Mathews bulled his way for the touchdown and then did the same for the two-point conversion to give the Eagles a 21-15 lead with 6:49 left to play.

"We've been so close in these situations before, and even though we always had confidence we could win these kinds of games, it's a great feeling to finally do it," Eagles receiver Jordan Matthews said. "This is a great confidence booster that will pay dividends the rest of the season."

NOTES: The Falcons were without two starters, both out with shoulder injuries -- CB Desmond Trufant (replaced by Jalen Collins) and TE Jacob Tamme (Levine Toilolo). ... Eagles LG Allen Barbre missed his second straight game with a hamstring injury. He was replaced again by Stefan Wisniewski. ... Eagles CB Aaron Grymes made his NFL debut on special teams after being promoted from the practice squad this week. Grymes, who wasn't drafted out of Idaho, spent the last three years playing for the Edmonton Eskimos of the CFL.