The home side's good play started at the back, with Chelsea's Nicolas Anelka often left redundant by Stephen Foster and Dennis Souza, who gradually became adept at forcing the lone marksman out wide.
At the other end, Tykes frontman Odejayi was a huge nuisance to the visitors, using his bulk well while holding and releasing intelligently.
The only concern for the home support was that he had not scored since September.
But he came close to ending that barren run during a 60-second spell that saw Simon Davey's side squander two good opportunities.
The first fell to forward Ferenczi, whose volley struck the foot of Cudicini's left-hand upright.
Moments later, Odejayi forced his way into the area only to see his low angled shot pushed away by the Chelsea shot-stopper.
Avram Grant's men were limited to half-chances, with Cole twice denied by the impressive Robert Kozluk, who got his body in the way on both occasions to prevent the England international from netting.
Odejayi celebrates his goal with Jamal Campbell-Ryce
Straight after the break, Cole was presented with his best opportunity to hand the visitors the lead, but once again his nemesis Kozluk did enough to force the midfielder to screw his shot wide from eight yards.
Chelsea cranked up the pressure in the second half, knowing that a replay would not benefit a team still fighting on two other fronts.
But try as hard as they did, the team lacked ideas and failed to carve open a stubborn Barnsley defence, even with the introduction of attacking duo Salomon Kalou and Claudio Pizarro.
And as Chelsea pressed forward, space was left at the back.
That space was exploited on the right wing by Devaney, who delivered a stunning ball to the far post for Odejayi to nod past the hapless Cudicini.
The Barnsley penalty area resembled the Alamo in the final 15 minutes, but somehow the home side held firm to book their passage into the last four.
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