The Norwegian manager was under pressure after the Hoops had crashed out of the Champions League play-off with a 2-1 aggregate defeat to Maribor in midweek, on the back of a 1-0 loss at Inverness last week.
The visitors found themselves up against it again with less than a minute played when James McPake headed in a Philip Roberts corner and as the Parkhead side struggled to find any rhythm, Roberts hit woodwork with a drive.
Substitute Leigh Griffiths, linked with a move to Hibernian, levelled 10 minutes after the break with a deflected drive and although Parkhead striker Anthony Stokes crashed a shot off the post, the home side spurned several chances to take the points.
Paul Hartley's side are unbeaten in five league games and were applauded off the park by their fans whereas the Hoops supporters were less than impressed by the outcome.
With the transfer deadline just over 24 hours away, there were other sub plots on Tayside.
Virgil van Dijk was missing from the Celtic side amid speculation that he is set to leave Parkhead.
The Dutch defender has been linked with several clubs including Southampton, Newcastle and Sunderland and was absent as Jason Denayer, Adam Matthews and Kris Commons returned, the latter as captain.
Celtic found themselves under immediate pressure when Dundee won a corner with just seconds played.
When Roberts' ball came in from the right, former Hibernian skipper McPake rose highest in the box to thunder in a header with Hoops midfielder Callum McGregor swinging and missing on the line.
A stunned Celtic side had a chance soon afterwards when Stokes got himself clear of McPake but his low drive did not have enough pace or power to really trouble Dundee keeper Kyle Letheren.
Thereafter the game opened up. Roberts left Parkhead left-back Emilio Izaguirre for dead as he burst into the box and Hoops keeper Craig Gordon got his finger tips on to the angled drive which hit the post before spinning to safety.
The champions remained vulnerable. In the 35th minute Hoops defender Efe Ambrose hesitated in dealing with a long Roberts pass, allowing Peter MacDonald in against Gordon but at a stretch he could only knock the ball wide.
Griffiths replaced Jo Inge Berget with four minutes of the first half remaining and in the last action of the half Stokes' free-kick made its way through a packed penalty area and forced Letheren into a fine save.
Defender Eoghan O'Connell started the second half in place of Matthews, with Ambrose moving to right-back but there was no immediate improvement.
The mood among the Hoops fans, however, changed in the 55th minute when Griffiths took a pass from O'Connell at the edge of the box and drilled in a shot which was deflected off Thomas Konrad and past Letheren and into the far corner of the net.
MacDonald and Gary Harkins were then replaced by Luka Tankulic and Simon Ferry immediately afterwards.
However, Celtic had the bit between their teeth, perhaps for the first time in the game.
Izaguirre, booked in the first-half for a late challenge on Roberts, might have counted himself lucky not to receive a second yellow for a foul on the same player.
In the 70th minute, as a re-energised Celtic side turned the screw, O'Connell headed a Commons corner past the post.
As the match stretched in the closing stages, Dundee substitute Martin Boyle, on for Roberts, had four chances on the break, only forcing Gordon into a save with the third one, a drive from 16 yards which resulted in a corner that came to nothing.
Tankulic fired wide from 25 yards before Stokes worked a one-two with Griffiths and crashed a shot off the post, before Letheren palmed a vicious drive from Griffiths round the post.
With two minutes remaining, Tankulic missed the target after he was set free by Boyle but the home fans forgave yet another missed opportunity as the final whistle sounded to signal the end of another good result for Dundee.