Bulgarian ace Berbatov produced the one moment of magic just before the interval with a superb volleyed effort to give Fulham all three points to move them further clear of trouble and add to Stoke's away day woes.
Jon Walters missed Stoke's best chance to score when he saw his second-half penalty saved by Mark Schwarzer to ensure the home side took the spoils.
Stoke fashioned their first opening of the game on seven minutes when Walters broke the Fulham offside trap to race clear on goal down the right and he fired in a shot which Schwarzer pushed out when finding Matt Etherington inside the box may have been the better option.
Fulham had a goal rightly disallowed on 10 minutes when Bryan Ruiz handled the ball into the net, with the Costa Rican earning a yellow card for his troubles from referee Lee Probert.
Steven Nzonzi, who picked up a nasty facial injury in an earlier clash with Berbatov, was lucky to escape a red card on 23 minutes when he appeared to slap Ruiz in the face, but Probert only booked the Stoke midfielder.
From the resulting free-kick Giorgos Karagounis fired in a powerful effort which forced Asmir Begovic to tip the ball over the crossbar.
Moments later Stoke suffered a blow when Etherington was forced off with an apparent back problem, with recent signing Brek Shea coming on for his debut.
Fulham made the breakthrough right on the stroke of half-time with a stunning effort from Berbatov. Sascha Riether's cross was not properly cleared by Robert Huth and the ball dropped invitingly to Berbatov who showed brilliant technique to smash his volley into the top corner past Begovic.
Fulham almost gifted Stoke an equaliser three minutes after the break when Philippe Senderos failed to clear his lines and Crouch stole in, but Schwarzer was quickly off his line to keep out the striker's effort.
Stoke won a penalty on 55 minutes when Ashkan Dejagah was adjudged to have handled Shea's cross inside the box and Walters, who has missed two spot-kicks already this season, saw his effort well saved by Schwarzer low down to his right.
Berbatov went close to grabbing a second goal just before the hour mark when he flicked the ball over Huth before firing in a left-footed volley which Begovic managed to grab hold of at the second attempt.