Kris Commons, James Forrest and Charlie Mulgrew fired Celtic to a comfortable 3-0 fifth-round win over Raith Rovers at Stark's Park.
The Hoops were knocked out of the Scottish Communities League Cup semi-final by St Mirren at Hampden last Sunday but there was little chance of another shock on Sunday, although the breakthrough did not come until the 56th minute when Commons scored from the spot after he was fouled by Raith defender Simon Mensing.
Irn-Bru First Division side Rovers ran out of steam and in the 82nd minute Forrest, on for Tony Watt, grabbed the second goal, with Mulgrew's fine strike four minutes later completing a solid afternoon's work by the visitors.
Gary Deegan scored his first ever goal for Hibernian as the Irishman's spectacular strike secured a 1-0 win over Aberdeen at Easter Road.
However, it was Hibs goalkeeper Ben Williams who was the true hero for the hosts, producing five excellent second-half saves as well as plunging to parry away a late Scott Vernon penalty.
Dundee progressed into the quarter-finals with a comprehensive 5-1 win over First Division Morton at Dens Park.
Barry Smith's side forgot about their troubles at the bottom of the SPL as their second-half surge saw off Allan Moore's men.
Strikes after the break from Lewis Toshney, Colin Nish, John Baird and Declan Gallagher saw them go through to the last eight after Michael Tidser had cancelled out Jim McAlister's opener to see the sides go in level at half-time.