The Blues looked to have overcame blustery conditions at Craven Cottage following the England international's spot-kick, yet they were pegged back late on by the American.
An end-to-end affair failed to produce any clear-cut chances for much of the first half, but the Blues entered the break a goal to the good after Frank Lampard slotted home a penalty following Stephen Kelly’s challenge on Salomon Kalou.
Despite a bright start after the interval, the visitors found themselves pegged for much of the second half, and Martin Jol’s men eventually found the equalizer after Clint Dempsey’s glancing header found the corner of the net.
Jol made just two changes to the side that triumphed over Bolton on Saturday. With Bryan Ruiz set to miss the remainder of the season after suffering a broken metatarsal in the win over the Trotters, Kerim Frei made just his ninth league appearance of the season.
Meanwhile, Danny Murphy was restored to the starting XI after overcoming illness, with Alex Kacaniklic dropping to the bench.
Perhaps with the FA Cup and Champions League semifinals in mind, Roberto Di Matteo made six changes to the side that beat Wigan at Stamford Bridge on Saturday. Lampard, John Terry and Ramires all recovered from knocks to replace David Luiz, Juan Mata and Daniel Sturridge.
Meanwhile, John Obi Mikel and Kalou started ahead of Michael Essien and Florent Malouda, and Fernando Torres was given the nod ahead of Didier Drogba.
A rain-soaked Craven Cottage was treated to an equally damp opening, as neither side managed to create any telling opportunities early on.
As the game wore on it was the visitors who began to take control, but they were reduced to long-range efforts with Mikel, Kalou and Raul Meireles failing to test Mark Schwarzer.
The warning shots sparked the home side into action, and Petr Cech had to be at his best to deny Dempsey and then the lively Kerim Frei.
A real ding-dong derby ensued, with the damp conditions lending themselves to counterattacking football, and it was the visitors who were granted a glorious opportunity to take the lead on the stroke of halftime.
Following some good footwork from Kalou, Kelly appeared to slightly clip the heels of the Ivorian forward, with the eagle-eyed Mark Clattenburg instantly pointing to the penalty spot.
Lampard stepped up and emphatically slotted his spot kick into Schwarzer’s bottom right-hand corner, notching his 150th Premier League goal and handing the Blues a potentially crucial halftime lead.
The Blues made a bright start to the second half with Lampard firing narrowly wide of Schwarzer’s right-hand post before coming within inches of latching onto Ryan Bertrand’s teasing cross.
Despite the visitors’ dominance, Frei continued to pull the strings for Martin Jol’s men, and it was his intelligent ball which set John Arne Riise away down the Fulham left.
The former Liverpool man opened up his body before striking the ball with the outside of his boot, yet his effort glided just inches wide of Cech’s far post.
With the home side beginning to take control of the game, Di Matteo introduced the ever-creative Mata in an attempt to find a second goal, but the Cottagers continued to press with wide-men Frei and Damien Duff looking increasingly dangerous.
Fulham was also looking dangerous from set-pieces, and Aaron Hughes produced a stunning save from Cech after he had eluded the Chelsea backline. However, the home side’s pressure eventually told from the resulting corner.
More lackluster Chelsea defending saw Dempsey find himself free in the area, and the American’s glancing header found the corner of the net after a slight touch from Gary Cahill.
The draw sees Chelsea move within two points of the final Champions League place, and Fulham moves level on points with Liverpool in ninth.