Two goals from John Hartson, bringing his season's tally to 21, and another from Chris Sutton eased Celtic into the quarter-finals and gave them their tenth win in a row, plus a fourth successive clean sheet for keeper Rab Douglas.
Dunfermline never gave up but neither their spirit nor their notorious plastic pitch, which prompted Hoops manager Martin O'Neill to leave out new signing Craig Bellamy, helped them to a first home win over Celtic since 1989.
The Fifers actually started the better in the opening five minutes but in Celtic's first attack, Sutton drove the ball into the six yard area and Hartson held off Andrius Skerla for a simple tap in.
Two minutes later Hartson rattled the woodwork with a ferocious shot and Sutton tucked away the rebound to continue his recent scoring run.
Derek Stillie's fine save from an Alan Thompson free-kick prevented further embarrassment for Dunfermline and they then enjoyed another decent spell, forcing six corners without ever seriously threatening.
Shortly before half-time a long ball was missed by the home defence and Hartson found the far corner of the net with a firm right footer.
The second period saw the visitors bring on Brazilian Juninho, veteran Paul Lambert and youngster Ross Wallace and, as the Glasgow side missed a series of chances on the counter attack, Dunfermline were unlucky not to pull a goal back.
Despite having had little to do Scotland keeper Douglas made two terrific saves from Skerla and substitute Noel Hunt.