Strikers Tony Stokes and John Guidetti found the net with Dundee hitting back with a landmark goal from David Clarkson.
The Hoops scored seconds before the interval when Kris Commons delivered a free-kick from the right touchline towards the front post and Stokes powered his header past Dundee keeper Scott Bain.
Dundee were opened up again nine minutes into the second half when James Forrest played a wonderful pass to the overlapping Adam Matthews and he picked out Guidetti with his low delivery for the striker to sweep his shot into the net.
But the visitors hit back just four minutes later when Clarkson became the first player in Dundee’s history to score in each of his opening seven games when he bundled the ball in from close range.
The Dark Blues started brightly and the unmarked Greg Stewart crashed his effort over the bar inside the opening minute.
And four minutes later Craig Gordon had to use his foot to deal with an awkward cross and Clarkson’s lob was cleared off the line by Virgil van Dijk.
Celtic finally responded when the returning Commons lost his marker inside the box to meet a Stokes corner at the near post but he glanced his header wide.
Forrest later played in Guidetti with a clever pass but the advancing Bain blocked the Swede’s shot.
Dundee squandered another great opportunity on 33 minutes when a corner from Gary Harkins was nodded back across goal by Clarkson but Thomas Konrad heads over from point-blank range.
After the goal flurry Celtic looked more assured and the came close with a clever free-kick routine in which Stokes laid the ball off the onrushing Charlie Mulgrew to shoot narrowly wide.
Stokes later found Calumn McGregor in the box but Bain saved the angled drive from the Celtic substitute.
Three minutes from time Emilio Izaguirre’s deep cross was headed wide by the normally reliable Guidetti.