The hosts made a bright start to the match, Bryan Ruiz taking an early shot for the hosts, but Mark Schwarzer had to make the first save of the game, after Jonathan Walters picked out Matthew Etherington in the Fulham box.
Berbatov also had an early chance, volleying his Sascha Riether's cross just high of the crossbar.
Steven N'Zonzi was left with a bloodied nose following a clash with Berbatov, but the Frenchman was able to continue, despite clearly being in some pain.
Stoke were forced into an early change as Etherington was hampered by a back injury, resulting in Brek Shea coming off the bench to make his first appearance for the Potters.
It looked like the sides would be heading into the break level, as two minutes of stoppage time came to an end, but the Bulgarian striker picked up the ball on the edge of the box from a Robert Huth clearance, volleying it past Begovic.
A scrappy final 15 minutes saw few chances for either side, but the physical play kept referee Lee Probert busy, booking three players in the opening 45 minutes.