Dundee striker David Clarkson extended his incredible goal-scoring run, but it wasn’t enough to earn the Dark Blues a Parkhead point.
The former Motherwell man became the one and only Dens Park player to have scored in his first seven games.
Clarkson’s second half strike proved only to be a consolation though.
By that point Paul Hartley’s men were 2-0 down.
On the balance of play and chances created, the league leaders were fortunate to take all three points.
Dundee settled into the game quickly, and certainly didn’t look intimidated by their surroundings, or their opposition.
Indeed, it was the visitors who were first to threaten.
Gary Harkins won a free-kick about 25 yards out, which he took himself.
It struck the wall, but the ball was sent back into the box and Clarkson tried to chip it over Craig Gordon. His effort was a half-hearted one and never looked like finding the net.
On 21 minutes Harkins picked out Paul McGowan unmarked beyond the back post. The former Celtic man controlled the ball well on his chest but would have been disappointed that he didn’t work Gordon with his shot, albeit from a tight angle.
There had been a couple of dangerous-looking Celtic corners but, other than that, Dundee were pretty comfortable.
Backing that up was the fact that it wasn’t until near the half-hour mark that prolific marksman John Guidetti got his first sight on goal.
And when he did, Scott Bain rushed off his line to close Guidetti down and block his shot.
Shortly after, there was a spell when Dundee had three chances in as many minutes.
The first of them was the best.
James McPake wasn’t picked up at a corner and when he headed the ball back into the six yard box, his fellow centre-back Thomas Konrad was also unmarked. He couldn’t keep his header on target though.
There was another corner a minute later, and this time Gary Irvine hooked the ball over the bar.
Then, with Gordon lying on the ground, a Greg Stewart shot from the edge of the box took a big deflection and looped just past the post.
Dundee’s good first half work was undone in the last minute of the 45 when Kevin Thomson gave away a free-kick on the bye-line. Commons swung the set-piece into the near post and Anthony Stokes headed home.
Ten minutes after the re-start you’d have thought this game was over as a contest when Celtic burst down the right and Guidetti gave Bain no chance from about 12 yards out.
The Dark Blues though hit back quickly to reduce the deficit back to just one.
They had a McPake header disallowed for offside and a hand-ball penalty claim waved away, but there could be no argument when top scorer Clarkson found the side of the net on 58 minutes.
For all that Celtic were far from their best, bar a stoppage time flurry from Dundee, they managed to see out the game without too much stress, and it finished 2-1.