The match ended in a draw after Bent's early opener was cancelled out by Fellaini's emphatic late equaliser taking Everton two points from the drop zone.
Sunderland should have led through Bent after just six minutes but he headed wide from six yards when he was completely unmarked in the middle.
Ten minutes later the opener came as Kenwyne Jones crossed for Bent and this time he found the corner with his header.
Everton pressed late in the first half and 10 minutes after the restart they could have been level as Louis Saha controlled a flicked-on corner and struck a shot with venom that flew just wide.
On the hour mark Sunderland almost sealed the game as they broke through Boudeweijn Zenden but his low drive was saved by Tim Howard down to his right.
The equaliser finally came with six minutes remaining as Tony Hibbert crossed for Fellaini who thrashed the ball into the top corner from 10 yards to give Martin Fulop no chance.