The League One outfit almost shocked the defending champions at Griffin Park by twice taking the lead but couldn't hold out for a famous fourth round triumph
Brentford enjoyed the better of the first half and deservedly went ahead through Marcelo Trotta after he turned home the rebound after Harry Forrester's initial effort was saved, but a goal shortly after half-time from Oscar brought the visitors back on terms.
However, just when Chelsea were on top, Turnbull inexplicably brought down Tom Adeyemi in the area allowing Forrester to convert the spot-kick and put the Bees in front, but a curled effort from Fernando Torres rescued the Blues late on.
Chelsea manager Rafa Benitez named a strong side including the likes of John Terry, Frank Lampard, Ramires and Torres, with Marko Marin and Turnbull handed rare starts.
Brentford boss Uwe Rosler placed his faith in the striking duo of Clayton Donaldson and young forward Forrester in the hope of forcing a cup upset.
The hosts settled into the game well, forcing their illustrious counterparts on the back foot and they went close when a defensive mix-up between Terry and Turnbull resorted in an indirect free kick inside the box which Forrester blazed fractionally over the bar.
The Bees forward came close for the hosts again just before the half hour mark as he wriggled past three players on the left flank before cutting inside and unleashing a fierce drive over Turnbull's bar.
That was followed by a good chance for Shaleum Logan who bent his effort just wide of the near post after cutting in from the left flank and later Forrester again, this time drilling a shot wide from 20 yards.
The breakthrough eventually came three minutes before half-time; it was Forrester again who stung the hands of Turnbull with a shot from range after dispossessing Frank Lampard, the Chelsea shot-stopper could only parry as far as Trotta, who made no mistake in drilling home the finish.
Benitez brought on Juan Mata for Marin after the break as Chelsea hoped to find a way back into the tie but Brentford picked up where they left off in the first half and managed to frustrate the visitors early on.
But the Blues weren't to be denied for long, Oscar plucked a looping ball out of the air just outside the box before stepping past one defender and prodding a clever finish past Simon Moore.
The visitors were invigorated by drawing level and began to pile on the pressure on the Brentford defence.
But just when Chelsea looked to have a grip on the game, Turnbull brought down Adeyemi as the Brentford substitute raced through on goal. Forrester stepped up and confidently tucked the penalty into the bottom left corner.
Brentford defended stoically to hold on to their lead but could do nothing about Torres' wonderfully shaped effort into the top corner in the 83rd minute after fine link-up play with Demba Ba.