Former Arsenal forward Jay Emmanuel-Thomas finished a move he started with a thumping finish to break the deadlock before playing a crucial role as Scott Wagstaff put the tie to bed with an accurate finish from outside the penalty area.
With top flight points on their minds Palace never looked like ending their Ashton Gate hoodoo which now stretches back 34 years and 11 visits, even after Owen Garvan's top-draw volley flew in with seconds remaining.
Belief around the ground that the Robins could record their first home win of the campaign was already growing after the announcement of the two teams.
Jack Dyer, the League Two club's third penalty taker in the shoot-out, saw his spot-kick saved by David Stockdale.
That miss came immediately after Bryan Ruiz had a lucky escape - his penalty striking the post but ricocheting into the back of the net off unfortunate Albion goalkeeper Dean Lyness.
John Arne Riise belted home the final penalty to send Martin Jol's Premier League team through - but not after a scare.
Fulham broke Burton down in the 36th minute through Adel Taarabt.
Dyer sent the tie into extra time with an equaliser after 85 minutes, and Burton went ahead in the 102nd minute through substitute Michael Symes.
It looked like Gary Rowett's side would mark their first ever League Cup tie at the Pirelli Stadium with a famous victory but Fulham substitute Hugo Rodallega levelled with three minutes remaining to send it to penalties.
League Cup results:
Barnsley 1 - 5 Southampton
Bristol City 2 - 1 Crystal Palace
Burnley 2 - 0 Preston North End
Burton Albion 2 - 2 Fulham * (Fulham win 5-4 on penalties)
Carlisle United 2 - 5 Leicester City
Derby County 5 - 0 Brentford
Doncaster Rovers 1 - 3 Leeds United
Huddersfield Town 3 - 2 Charlton Athletic
Leyton Orient 0 - 1 Hull City
Liverpool 4 - 2 Notts County
Norwich City 6 - 3 Bury
Peterborough United 6 - 0 Reading
Queens Park Rangers 0 - 2 Swindon Town
Sunderland 4 - 2 Milton Keynes Dons
Tranmere Rovers * 1 - 1 Bolton Wanderers (Tranmere win 4-2 on penalties)
West Ham United 2 - 1 Cheltenham Town
Yeovil Town 3 - 3 Birmingham City * (Birmingham win 3-2 on penalties)
West Bromwich Albion 3 - 0 Newport County
- Sports & Recreation
- Burton Albion
- Scott Wagstaff