The home side defended heroically to put another spanner in the works for Chelsea's season.
Joe Cole missed the best chance of the game for Chelsea, firing wide from 6 yards, whilst midway through the first half, Barnsley's Istvan Ferenczi saw his half-volley rebound back off the post and out of play.
The Tykes took the lead on 66 minutes, when Odejayi converted Martin Devaney's superb cross past Carlo Cudicini from close range.
John Terry blazed over late on as Chelsea searched for an equaliser, but the home side hung on to claim the biggest scalp of the round, and send them through to their first semi-final for over 80 years.
After the match, Barnsley boss Simon Davey hailed his players for the fantastic performance they put in.
"I can't believe it. We beat Liverpool and they thought we couldn't do it again," he said.
"But I thought we could and the players were fantastic again. Kayode came out tops again - I'm so pleased for him."