Georgios Samaras sent Celtic on their way to a fifth consecutive SPL victory with an overhead kick 16 minutes into a one-sided first half at Dens Park.
Dundee made a game of it after the break and Colin Nish missed a great chance to equalise but Gary Hooper secured the points in the 71st minute when he lobbed Rab Douglas.
Celtic controlled the final stages as they extended their lead at the top of the table after second-placed Inverness were earlier held by St Mirren.
That result, plus Ross County's win at Hibernian, left Dundee nine points behind at the foot of the table.
Stephen O'Donnell had the first shooting opportunity in the ninth minute when he pounced on Emilio Izaguirre's poor clearance and sent a curling effort just over the top corner from 20 yards, but that was as good as it got for the hosts in the first half.
Charlie Mulgrew swung the set-piece in and Efe Ambrose met it first-time but his shot bounced off the bar from six yards and Victor Wanyama volleyed the rebound over.
Hooper, who started the match at the head of a midfield diamond, shot just wide from 25 yards before Celtic took the lead. Another inswinging corner from Mulgrew caused problems and Watt fired a shot from beyond the back post that Douglas pushed on to the bar. The rebound fell eight yards out and Samaras hooked the ball over his head and into the top corner.
Celtic were in complete control and switched to a 4-3-3 with Hooper pushing forward through the middle but they could not create any more first-half chances despite their superiority in possession.
Dundee showed more signs of attacking intent as the second half started and Nish should have equalised in the 50th minute. The hosts worked the ball from right to left and Ryan Conroy's cross from the by-line was inch perfect for the unmarked Nish five yards out, but the former Hibernian striker could not guide his header far enough away from Fraser Forster.
Dundee kept the pressure on and Celtic manager Neil Lennon made a change in the 61st minute when he brought on James Forrest for Kayal and switched to a more orthodox 4-4-2 with Samaras moving to left midfield.
Douglas denied Celtic a second four minutes later when he stopped an attempted clearance by Kyle Benedictus slicing into his own net following Lustig's near-post cross.
But Hooper was soon celebrating when Lustig's lofted ball up the right bounced over Declan Gallagher's head and the former Scunthorpe striker lobbed Douglas from 16 yards.