Celtic booked their place in the quarter-finals of the Scottish Cup with a 3-0 win at Raith Rovers on Sunday.
Neil Lennon's side were made to work for their victory against Rovers, who sit sixth in the First Division.
The Scottish Premier League leaders went to the half-time break without the lead after a goalless opening stanza.
But the entire complexion of the match changed on 56 minutes when Kris Commons tucked away a penalty to give the visitors the lead.
Substitute James Forrest made sure of the win with his goal seven minutes from time and Charlie Mulgrew added to the score-line with a late strike.
Dundee might be on the bottom of the Premier League but they thrashed First Division outfit Greenock Morton 5-1 at Dens Park.
Dundee claimed the lead after 29 minutes when Jim McAlister scored the opener.
But it lasted just two minutes as Michael Tidser produced a quick reply for the visitors.
Dundee put on a clinic in the second half though as Lewis Toshney, Colin Nish, John Baird and Declan Gallagher all scored.
The day's other match saw Hibernian edge Aberdeen 1-0 thanks to a second-half goal from Irishman Gary Deegan.