The Patriots now await the winner between the Pittsburgh Steelers and Jacksonville Jaguars, who play tomorrow for the remaining spot in the AFC Championship match.
It wasn't an ideal start for the Eagles, who had a bye last week during the wildcard round, as they looked to take down a side who were in the Super Bowl a year ago.
While the Eagles came into the playoffs as the top seed in the NFC, with first-string quarterback Carson Wentz out injured, they went into the match as underdogs and found themselves down 3-0 early following the fumble which led to a Matt Bryant field goal for Atlanta.
The Eagles took the lead off the Falcons early in the second quarter when running back LeGarrette Blount charged over on fourth and goal. However, a fourth fumble saw the Eagles go into halftime trailing after a turnover deep in Philadelphia's half gave the Falcons great position and they capitalised through a short reception by Devonta Freeman to take a 10-9 lead at the break.
Neither team could find their way into the end zone in the second half, however two field goals from Philadelphia kicker Jake Elliott proved the difference as the Eagles took a 15-10 win to move into the NFC championship.
The Patriots also got off to a mediocre start, with the Titans getting on the board first through a touchdown to wide receiver Corey Davis.
But that was all Titans fans had to cheer about as the Patriots offence took control.
A 21-point second quarter saw quarterback Tom Brady find Chris Hogan and James White in the end zone, as well as White getting across the plane on the ground. Those three touchdowns put New England up 21-7 at halftime.
The Patriots added to the hurt with a touchdown to Brandon Bolden in the third to push their lead beyond the reach of the Titans, with a late touchdown by tight end Rob Gronkowski sealing the deal.