It was a laboured first half from the Blues as Fulham's defence were not really tested and it took until midway through the second half before somebody told the players there was a West London derby on for it to kick into gear when both sides had scored.
Chelsea took the lead through something out of nothing two minutes into the second half when Fernando Torres controlled an aerial ball at the top of the area which fell to fellow Spaniard Juan Mata who hooked it across his body and into the bottom corner of the net with aplomb for number four this campaign.
Fulham got back on level terms less than ten minutes later when Philippe Senderos made a positive run forward before eventually getting it out to Bryan Ruiz who pulled it back from the right for Clint Dempsey who tucked it away at the front post for his ninth of the season.
Earlier chances came when Fulham's Orlando Sa, who was given a rare start, really should have scored when Stephen Kelly supplied a nice cross from the right but the Portuguese put his header from the edge of the six-yard box over the crossbar in the 14th minute.
Moments later, Chelsea had their best chance of the first half when Mata found Torres in the area with a lofted ball which the former Liverpool man controlled brilliantly with his chest before getting a volley off but it was hit straight at David Stockdale who came up with a reflex save.
In the 65th minute, Daniel Sturridge forced Stockdale to tip over with a curling effort before an unmarked Florent Malouda was denied when he tried to backheel John Terry's header from the ensuing corner with the Cottagers gloveman again doing well.
Late in the contest, Raul Meireles was denied with a late shot on target moments before Drogba's front post glancing header was parried away by Stockdale prior to Petr Cech keeping out Pajtim Kasami and then Fulham keepr Stockdale again doing the business when he palmed over a dipping Drogba free-kick.
The result was not the one Andre Villas-Boas was looking for as Chelsea missed the chance to move above Tottenham into third whilst Martin Jol will head back around the corner to Craven Cottage with a well-deserved and potentially unexpected point as his side remains 13th.
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