The Eagles did not resemble the NFL's second-ranked defense in the first half as the Bears amassed 207 total yards and built a 13-7 lead.
But the Eagles turned the game around after halftime, forcing a turnover and holding the Bears to nine total yards on their first five possessions.
"I thought our defense played very well," Eagles Coach Andy Reid said. "We played better in the second half and the coaches made some changes that worked out well."
"We just calmed down and played football," Eagles defensive end Hugh Douglas said. "The biggest thing that happened is they kept us off-balance and got some good runs. But we stayed calm and played our defense."
While the defense was doing its part, Akers kicked field goals of 23, 36, 27 and 22 yards in the second half.
The Bears reached the Philadelphia 25 with a first down in the game's final minute. But Jim Miller threw three incompletions around a sack.
Miller's final incompletion into the end zone capped a frustrating afternoon for the Bears (2-6), who were penalized 12 times for 121 yards as they suffered their sixth straight loss. Philadelphia was flagged six times for 54 yards.
"I don't have an answer for you on a lot of those things," said Bears Coach Dick Jauron about the penalties. "We will definitely have to see them on tape. I'm not watching what they (the referees) are watching. We never agree on everything. You've got to believe the officials are awefully good at what they do."
"I told the guys during the game to not be gun-shy," Bears defensive coordinator Greg Blache said. "I'm not going to tell you exactly what I said (to the officials), but I told them to let us play football. Its unfortunate that there were so many penalties called in coverage, but I haven't looked at the film so I am not going to comment. I don't want to get fined."
Philadelphia quarterback Donovan McNabb ran five yards for a touchdown in the second quarter to help the Eagles (6-2) win their third straight game.
Last season, the Eagles eliminated the Bears in the divisional round of the playoffs with a 33-19 victory at Solidier Field.
Holding a 16-13 lead with under nine minutes remaining, the Eagles squandered a chance to build on the advantage. On fourth and one from the Chicago 24, Eagles coach Andy Reid elected to go for it and Duce Staley was stuffed for no gain.
Staley, who rushed for a combined 288 yards in the last two weeks in wins over Tampa Bay and the New York Giants, was held in check as he managed just 39 yards on 19 attempts.
"You have to give credit to them," Staley said. "They are a good defense. They play hard and were giving us different looks in the red zone that we didn't adjust to. But a win is a win."
After the big stop, the Bears managed one first down before being forced to punt.
McNabb completed a 39-yard pass to Todd Pinkston down the left sideline on the ensuing possession, giving the Eagles the ball at the Bears 14. On fourth and inches at the five, Reid opted for the field goal this time and Akers converted from 22 yards for a 19-13 lead with 3:42 to play.
Akers kicked a 27-yard field goal 1:31 into the fourth to snap a tie after end Brandon Whiting recovered a fumble by receiver Dez White on a running play at the Chicago 18.
That gave the Bears, who had managed just two first downs in the second half, a chance to rally.
Miller, who had missed the last two games with tendinitis in his right elbow and shoulder, hit his first four passes on the ensuing drive as the Bears reached the Eagles 26. On fourth and one, Leon Johnson powered up the middle for two yards to keep the drive alive.
But Miller threw two incompletions before being sacked by end Hugh Douglas for a nine-yard loss on third down. In last season's playoff meeting, Douglas knocked Miller from the game in the second quarter with a separated shoulder and later drew a $35,000 fine from the NFL.
On fourth down, any chances for a comeback were lost when Miller's pass fell incomplete out of bounds in the end zone. Miller finished 19 of 35 for 205 yards, but threw for just 70 yards after halftime.
Playing one on one on the outside and leaving star middle linebacker Brian Urlacher to shadow McNabb, the Bears contained the Eagles' star quarterback.
McNabb went 18 of 33 for 209 yards and an interception and rushed for 46 yards on nine attempts. He did pass for 133 yards after halftime. Urlacher finished with 10 tackles and a sack.
"They were blitzing a little bit and doing what we call a `Mush Rush,'" McNabb said. "Guys were just floating around the line of scrimmage, keeping Urlacher as my spy. And they gave us some holes, and that's what we hit. We were able to exploit those holes a littlle bit and hit some guys over the middle."
"I spied him a little bit when he wasn't running," Urlacher said. "Our plan was to keep him in the pocket and make him beat us with his arm."
After a scorleess first quarter, the Bears broke on top 5:32 into the second on a 30-yard field goal by Paul Edinger.
But the Eagles answered on their ensuing drive, moving 73 yards in 10 plays. The drive was aided by three penalties that totaled 30 yards.
McNabb capped the march by calling his own number on a draw and scoring on a five-yard run, making it 7-3 with 4:42 left in the half.
The Bears answered with a seven-play, 69-yard drive. Anthony Thomas capped the drive by scoring on a six-yard run around left end with 77 seconds left in the half.
Thomas rushed for 51 yards in the half, but managed just one on five carries after intermission.
McNabb was intercepted by safety Mike Brown inside Chicago territory with under a minute left in the half and Miller quickly orchestrated a scoring drive.
Miller found Ahmad Merritt for 25 yards and Marcus Robinson for 12 more, moving the ball to the Philadelphia 35. On the final play of the half, Edinger connected on a 53-yard field goal with the ball hitting the crossbar before bouncing over.
Akers kicked a 23-yard field goal on the ensuing possession of the third quarter, pulling the Eagles within 13-10. He connected from 36 yards on the next possession to tie it.