There is an idea in the NFL of a team playing "spoiler" or a team doing another a favor. For the Packers and Eagles, a relationship formed in the design of both teams' playoff runs. Philadelphia took care of Green Bay's division foes, while the Packers secured a massive comeback win over the Eagles only competition for the NFC East crown.
The Eagles were able to get key victories for their playoff run against the Lions and Bears. While the victory over the Lions certainly did not eliminate them from NFC North contention, it allowed the Packers to stay even with quarterback Aaron Rodgers out with an injury. Also, the Packers could have been eliminated had the Bears won the Week 16 matchup against the Eagles. Instead, Philadelphia dominated Chicago in a game that meant more to the Bears and Packers than it did to the Eagles. This allowed for the Packers to play in a "winner takes all" matchup against the Bears in Week 17.
On the flip side, the Packers comeback/upset victory over the Cowboys in Week 15 saved the Eagles from an early elimination with a possible loss to the Bears. The 37-36 win over Dallas allowed the Eagles to stay in the fight until Week 17, no matter the consequences of the Chicago-Philadelphia matchup later on in the schedule. With the Philadelphia loss to the Vikings, Cowboys wins against the Packers and the following week against the Redskins would have dealt the Eagles a striking to their playoff hopes if combined with a loss to the Bears. Instead, the Packers won and the Eagles were able to continue to control their own destiny (so to speak, sorry Chip!).
With the help of each other, both teams were able to vanquish their foes and win their respective divisions. While they are now on their own with their playoff missions, it clear that both teams greatly benefited from the each other's success.