Blues triumphed in a game that had thrills, spills, penalty misses and early baths. Anelka and Baines missed their spot-kicks, whilst Turnbull and Drenthe saw redChelsea progressed to the quarter-finals of the League Cup at the expense of battling Everton in a crazy encounter that saw both sides finish with 10 men.
The opening stages of the game ebbed and flowed with both teams coming close to opening the scoring. Chelsea's Romelu Lukaku had a second minute shot drift wide before Everton's Louis Saha made goalkeeper Ross Turnbull work twice inside the first 10 minutes.
Josh McEachran caused mayhem in the Toffees' box after quarter of an hour, his shot was blocked by Sylvain Distin before being brought down for a penalty by Johnny Heitinga. But Nicolas Anelka missed the spot kick and gave the home side respite.
Lukaku and Bilyaletdinov exchanged chances before Salomon Kalou opened the scoring after 37 minutes from just outside the area after good work by Ryan Bertrand. The attacker's chipped shot was missed completely by Jan Mucha who tried to claw it back before it went over the line but failed.
The second half proved to be even more entertaining than the first, with Kalou and Anelka testing a nervy Mucha before his opposite number Turnbull was sent off for bringing down Saha just after the hour.
Andre Villas-Boas responded by bringing on No. 1 Petr Cech just in time for the penalty and the Czech would perform superbly to block Leighton Baines' effort.
The home side started to take control of proceedings with their one-man advantage and came close to equalising through Royston Drenthe, but his shot just went over. With seven minutes remaining, however, Louis Saha headed in subsitute Seamus Coleman's cross as the hosts' pressure finally paid off.
Royston Drenthe and Denis Stracqualursi both went close to putting the Toffees in front and Seamus Coleman hoofed a Florent Malouda chance away at the other end in the dying embers of regular time.
Extra-time saw the hosts reduced to 10 men as well, as Drenthe's over enthusiastic challenge on Bertrand gave Chelsea the impetus.
Daniel Sturridge ultimately proved the match winner, tapping in from close range after Mucha could only parry Florent Malouda's long-range drive, seeing the visitors in the hat for the next round.