Atlanta (6-9) next meets Carolina (6-8-1) for the NFC South title next week in the Georgia Dome. The Saints (6-9) are left with an anticlimactic visit to Tampa Bay.
Graham's fumble came on the first play of the fourth quarter. The star tight end leaped to grab Drew Brees' pass and came down at the goal line, his body writhing as he tried to force his way past reserve safety Dezmen Southward. Fellow Falcons safety Kemal Ishmael converged immediately and ripped the ball away, then recovered it.
Graham's forward progress appeared to have been stopped before the ball came loose, but that was not reviewable.
At least one replay angle showed that the ball may have broken the plane of the goal line, and the Superdome crowd roared when it was shown on large video boards. However, referee John Parry could not find evidence conclusive enough to overturn the call. Parry's announcement spawned a cascade of boos from anxious Saints fans, whose team remained down 20-7 with its playoff hopes fading.
"There was nothing clear and undisputable to make a change to the ruling from the field," Parry said.
Graham was not present when locker rooms were opened to reporters.
Southward said he never had a good look at whether Graham got in.
"I was too busy putting my face in his ribs. I was just trying to keep him out," Southward said. "All that credit goes to Kemal, obviously coming in and not quitting on the play."
Brees said he thought Graham scored, calling the consequences of the ruling, "huge."
While the play was a momentum changer, Atlanta might have won anyway.
After not practicing or playing for about two weeks, Jones caught seven passes for 107 yards.
"I felt OK. I know I needed to be out there with my teammates," Jones said. "When the ball is in the air, I got to get it. I don't hear nothing. I don't feel nothing."
Jones made his presence felt with one double-digit-yard reception after another, including third-down catches of 12 and 24 yards during the Falcons' first touchdown drive.
The Saints committed three turnovers in the fourth quarter in their fifth straight loss at home and were eliminated officially with Carolina's victory over Cleveland.
Seeking to fire up the home crowd in a crucial game, the Saints changed their introductions, turning off the house lights during a pyrotechnic display while fans held up their mobile phones as if at a concert.
Notes: Falcons running back Steve Jackson (quad), safety Williams Moore (shoulder) and cornerback Josh Wilson (hamstring) all left the game and coach Mike Smith did not update their status. ... The Saints lost five straight at home in the same season for the first time since 1980, when Archie Manning was quarterback and New Orleans went 1-15.
Copyright 2014 by The Associated Press