Late goals from Robin van Persie and Michael Carrick helped United cancel out a Steve Sidwell opener to lead a resolute Fulham 2-1 before Bent headed in at the far post to nick a point in the 94th minute.
A stunning finish from revitalised striker Emmanuel Adebayor helped fifth-placed Tottenham sink Everton to move above their rivals.
Tottenham were second best for most of the match as Everton confidently dominated possession but they were left to rue their lack of a cutting edge when Adebayor fired powerfully into the bottom corner midway through the second half.
It was the Togo striker's sixth goal in his last eight league matches.
Tottenham, who had won just two of their previous 13 league games against Everton, have 47 points, three adrift of fourth-placed Liverpool and two ahead of Everton in sixth.
Manchester United are seventh on 41 points while Fulham stay bottom with 20.
