Dempsey's goals were sandwiched between a pair of goals by Chelsea's England star, Frank Lampard.
The American scored in the 10th minute when he connected on Simon Davies' free kick and rose above the Chelsea defense in the 89th minute to score a superb equalizer.
In his second full season at Fulham, Dempsey has been consistently starting on the outside. His four goals are only two less than he scored in all the 2008-09 EPL campaign. His solid play mirrors that of the Cottagers, whose nine-game unbeaten streak -- the longest by any team in the EPL this season -- put them in ninth place at year's end.
Another surging team is Everton, which moved into sixth place with a 3-0 win over Sunderland on Sunday. The shutout was the fourth in a row for American goalie Tim Howard. On Friday, Howard was outstanding in a 1-0 win at Middlesbrough.