Caretaker boss Ray Lewington made two changes to Lawrie Sanchez's final side, bringing in a pair of his summer signings, Paul Konchesky and Diomansy Kamara, while Wigan boss Steve Bruce suffered a blow before kick-off as Emile Heskey failed to recover from an ankle injury sustained in last week's stunning 5-3 victory over Blackburn.
And it was the hosts who made the better start, Titus Bramble twice being forced to make last-ditch interceptions as Carlos Bocanegra and Kamara went close from Danny Murphy corners.
Dempsey and Simon Davies were then inches away from converting Hameur Bouazza's cross as Fulham piled on the pressure.
But after weathering the storm, Wigan came out of their shells and Ryan Taylor swung over a devilish cross that slid past the far post, before Davies forced visiting keeper Chris Kirkland into a sprawling save from his rasping drive.
Kamara then missed the chance of the half, poking agonisingly wide after beating Kirkland to Davies' free-kick, before Konchesky rattled the bar with a swerving 35-yard effort that would have been good enough to win any game.
The game then drifted as two sides relatively short on confidence relied on route one tactics rather than the passing game, which had provided the few moments of genuine quality.
And Lewington made a double substitution on the hour in a bid to liven the game up, bringing on David Healy to switch to three up front, but it was Wigan who took the lead with 20 minutes to go.
Bent showed he is a striker in form after a hat-trick last week with a predatory finish after Bramble flicked on former Fulham captain Michael Brown's lob.
But it was Dempsey, one of the few successes in Fulham's season, who equalised with 12 minutes left, coolly sliding home his fifth of the season after Kamara's cross-shot fell to him 12 yards out.
With both sides pushing for a winner Antoine Sibierski landed a header on the roof of the net for Wigan, but in truth neither side deserved to take all three points after a disappointing game that proved why both are relegation candidates.