Martin Jol will return to former club Tottenham on the last day of the season knowing the Cottagers lie one point shy of their previous record, secured under Roy Hodgson in the 2008/09 season.
If the west Londoners achieve the feat, much of the praise will be deservedly directed at Dempsey in a season that he has netted 23 goals in all competitions.
The United States international’s future may be in doubt but it did not stop him scoring at Craven Cottage on Sunday, firing home a superb 25-yard free-kick after 12 minutes.
Phil Bardsley temporarily brought the visitors level with an excellent strike only for Fulham to respond immediately, with Mousa Dembele seeing a 20-yard strike take a slight deflection off Michael Turner as it flew home.
The introduction of substitutes Nicklas Bendtner and Frazier Campbell saw Sunderland end on a high but they could not find a way past Fulham, who secured their fifth win in seven games to leave them with a record-equalling seventh-place finish within grasp.
The Whites were boosted heading into the game by the return of manager Jol, who missed the recent trips to Everton and Liverpool through a chest infection.
The Dutchman brought Mahamadou Diarra in for Alex Kacaniklic to face Sunderland, who drafted in Ji Dong-won, Simon Mignolet and Craig Gardner into the starting line-up.
The visitors started brightly on the banks of the Thames but Fulham soon found their feet.
Having seen Pavel Pogrebnyak come close to connecting with a Damien Duff cross, the latter latched on to a superb long ball from the back only to see a well-struck effort smothered by Mignolet.
The early attacking impetus translated into the opening goal in the 12th minute when Fulham were awarded a free-kick 25 yards out.
Lee Cattermole blocked off Diarra and top scorer Dempsey stepped up to fire a right-footed effort with pace and swerve into the top corner.
The lead was almost wiped out four minutes later, though, as Stephane Sessegnon broke into the area, with only indecision and superb goalkeeping from Mark Schwarzer thwarting the Benin international.
The Cottagers were soon back on the offensive in search of a second, which would have come through Pogrebnyak had Turner not been alert to block his goalbound strike eight yards from goal.
The game burst into life after 34 minutes when Bardsley finished a move he started.
The defender burst forward and collected a Ji cutback to fire home a right-footed thunderbolt from outside the box.
Sunderland, though, were not celebrating for long as Dembele fired an instant reply.
The much-vaunted Belgian broke from the halfway line and unleashed a 20-yard effort that took a slight deflection off Turner and flew into the top left-hand corner.
The Cottagers were chomping at the bit as they looked for a third and Duff fired into the side-netting, before the visitors came close through a Gardner free-kick.
It was Fulham that ended the first half the stronger and they continued in the same vein after the restart.
Pogrebnyak saw an effort deflect behind by John O’Shea and only a goal-line clearance from Jack Colback prevented Dempsey scoring a deft curling effort from the resulting corner.
Right-back Stephen Kelly joined in with the action by testing Mignolet with a fierce drive, before the Sunderland goalkeeper got down well to parry a stinging Duff shot.
O’Neill brought on Bendtner for Ji in a bid to change the course of proceedings but Fulham were still on top, with Dempsey hitting the wall with a free-kick from a good position.
The Black Cats began to grow into the game following the introduction of the on-loan Arsenal striker, who was soon joined in attack by Campbell – on for Matthew Kilgallon.
The Whites were spending a lot of time on the back foot but came close to extending their lead when Dembele was put through one-on-one with Mignolet, although the Sunderland keeper produced a superb save.
The visitors returned to the attack immediately, though, as Campbell put through fellow substitute Bendtner, who could only curl wide when well placed.
The pair linked up again shortly afterwards as the latter’s cushioned header set up Campbell, who could only lash wide from close range.
Turner headed straight at Schwarzer as Sunderland continued to press, before the hosts replaced Pogrebnyak and Murphy with Kerim Frei and Chris Baird.
Dembele saw a shot saved smartly by Mignolet as the clock wound down, before Schwarzer produced a superb save to prevent Campbell in stoppage time.