In midweek Celtic defeated Raith Rovers 2-0 to book a place in the last eight of the League Cup.
Between league matches against Dundee and Hearts the cup tie was low key with goals from Kris Commons and Stefan Johansen ensuring a home win.
It was hardly inspiring stuff but Commons first half strike calmed some nerves before Johansen put the tie beyond Raith with a late solo goal bursting from midfield.
After the match Ronny Deila admitted: “I am always a little bit worried. You never know in football and the cup is always like that.
“When it is 1-0 anything can happen but I think we were in good control and it was good that we got the second goal.
“When you meet a team from a lower division it is always difficult because they gave 110 per cent and sometimes it is easy to get a bit lazy, if I can say that.
“But I think our players worked really hard for 90 minutes. We kept the pressure on all the time and could have scored more.
“We kept another clean sheet which is very important but every team can get one chance and they should get credit for hard work and defending very well.”
Deila made six changes to the side that had beaten Dundee three days earlier and is likely to again make a number of changes for today’s match with Hearts.
Most attention will be in defence with supporters hoping to see Jozo Simunovic make his home debut.
With Virgil van Dijk and Jason Denayer no longer at the club Simunovic is expected to step into central defence and provide the type of leadership that earned van Dijk his move to Southampton.