Andre Villas-Boas’s side were on course for some much needed festive cheer when Juan Mata put the hosts ahead in the second half, but Dempsey levelled soon after to leave the Blues 10 points behind City.
Chelsea’s hopes of mounting a serious challenge for the title are starting to fade after a third successive draw and even a place in the top four can’t be taken for granted as they will slip to fifth if Arsenal beat Wolves on Tuesday.
The Boxing Day draw was far more rewarding for Fulham, who moved five points clear of the relegation zone and spoiled their local rivals’ Christmas in the process.
Villas-Boas handed Fernando Torres a rare start ahead of Didier Drogba and the Spanish striker went close with a fierce drive that forced a good save from David Stockdale.
After a lacklustre first half, it was Chelsea who took the lead two minutes into the second period when Spanish playmaker Mata drilled his shot past Stockdale.
Fulham were thrashed 5-0 by Manchester United last week and Mata’s goal could have been the trigger for another meltdown from the Cottagers.
But Martin Jol’s side, looking for their first win at Stamford Bridge since 1979, hit back with an equaliser in the 56th minute as American midfielder Dempsey tapped in after Bryan Ruiz got past Ashley Cole to whip over a cross that Petr Cech failed to claim.
Chelsea pressed for a winner, only to see Stockdale make fine saves to deny Daniel Sturridge and Florent Malouda.
Manchester City travel to West Brom later on Monday, while second placed Manchester United are at home to Wigan and Liverpool host bottom of the table Blackburn.