Scott McDonald led the way as Celtic showed their determination to hold onto the Co-operative Insurance Cup by dumping Falkirk out 4-0, while arch-rivals Rangers progressed beating Queen of the South 2-1.
The striker helped himself to a double on a night when several fringe players also shone for the Hoops, with Pat McCourt netting his first goal for the club and Chris Killen completing the rout.
Falkirk did strike the woodwork late on but the outcome never appeared in doubt as the holders cruised into the quarter-finals.
Steven Naismith's first-half strike and a late counter from substitute Nacho Novo ensured Rangers won an uneasy tie at Palmerston Park.
Naismith had the easiest of tasks in knocking into the empty net in the 16th minute after Kris Boyd had set him up following a defence-splitting pass from Pedro Mendes.
The Irn-Bru First Division side rallied but striker David Weatherston missed good chances either side of the interval before Novo, on for Jerome Rothen, sealed the tie with 11 minutes remaining although Robert Harris grabbed a consolation in the dying seconds.
A controversial penalty helped Hearts into the quarter-finals as Michael Stewart completed their comeback in a 2-1 win over Dunfermline.
Hearts manager Csaba Laszlo had warned against a repeat of last season's home defeat by Dunfermline's Irn-Bru First Division rivals Airdrie, but they trailed to Graham Bayne's goal at half-time.
However, Suso Santana headed an equaliser despite the visitors' appeals over an earlier infringement, and Hearts moved in front in the 74th minute after Brian Winter adjudged Neil McGregor to have fouled David Obua.
McGregor claimed his challenge was a fair shoulder charge but Stewart sent Hearts through.
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