The late drama left the Blues three points behind leaders Liverpool in the Premier League table.
Chelsea thought they had fought back to win the west London derby after Frank Lampard scored twice in the second half to cancel out Dempsey's 10th minute opener.
But the American midfielder's second of the day, heading home a Simon Davies corner, stunned Luiz Felipe Scolari's side and leaves them only seven points ahead of Manchester United, who have three games in hand.
Chelsea also saw both defender Alex and winger Florent Malouda limp off with hamstring problems to add to a miserable afternoon for the Blues.
In a dramatic match played just minutes after Liverpool had thumped Newcastle United 5-1, Fulham stunned their derby-day opponents by going ahead after just 10 minutes.
Davies floated over a free-kick from the left and Chelsea allowed the ball to bobble around before Dempsey deftly flicked it home at the far post with goalkeeper Petr Cech and his defenders still rooted to the spot.
At the other end, Didier Drogba, who shot wastefully into the side-netting with the score still 0-0, dragged another excellent chance wide after 19 minutes and Chelsea were then hit by a double injury blow.
Malouda limped off injured to be replaced by Nicolas Anelka after 30 minutes and Alex followed suit, replaced by Ricardo Carvalho, who has missed the last 13 games with a knee problem.
Chelsea's response was a flurry of corners and two stinging shots from Lampard that were well saved, but it wasn't enough to prevent Fulham going into the break 1-0 ahead.
In the end it took a terrible mistake from the home side to change the scoreline.
Chelsea came out firing in the second half and when Drogba challenged with Aaron Hughes from Joe Cole's chipped pass, Fulham's defence was left floundering.
Hughes hesitated, keeper Mark Schwarzer didn't come and Lampard pounced to tap home the rebound.
That was a major turning point in the game because, with Lampard hitting top gear, Chelsea suddenly found their stride.
Joe Cole was denied by a double save from Schwarzer before Lampard eventually made it 2-1, firing home a trademark long-distance free-kick after Andrew Johnson had foolishly produced a high challenge on Deco 25 yards out.
Chelsea thought they had won it but when Davies swung over a late corner, Dempsey headed home and Fulham celebrated a famous result.