Gary Mackay-Steven and Virgil van Dijk- with an absolute beauty – earned the points that keeps the champions on course to retain their title, Jim McAlister pulling one back with three minutes of normal time left.
The Hoops, smarting from their shock – and controversial – 3-2 defeat to Inverness in the semi-finals of the Scottish FA Cup at the weekend, were rarely troubled by the hosts, and from the moment Mackay-Steven gave them the lead, victory looked assured.
The winger served warning early on, chesting the ball down and firing a volley a couple of feet over the bar from the edge of the box after a corner was cleared.
Van Dijk was the first to test Dundee keeper Scott Bain, but his looping back-post header from a corner was comfortably gathered.
Celtic then had a big shout for a penalty when James Forrest went down in the box after Bain fumbled a corner, but the visiting fans’ claims were ignored.
Leigh Griffiths shot into the side-netting, but on 34 Mackay-Steven got the opener.
Stuart Armstrong’s free-kick was headed back across goal by van Dijk, and when the ball fell for the former Dundee United man on the edge of the box, he controlled it with his first touch, then walloped it into the top corner with his second in front of the visiting fans.
Forrest then shot straight at Bain from just inside the box as Celtic pressed for a second before the break.
Nir Biton curled a venomous 25-yard effort just wide after the interval, and Dundee finally threatened at the other end, but James McPake slipped as he unleashed his shot and Craig Gordon gathered easily.
Bain had to parry an effort from Griffiths, but the killer second goal arrived on 63.
McPake gave away a free-kick for a foul on Stuart Armstrong and van Dijk smashed home the free-kick – a near-identical copy of his goal against Inverness.
Dundee pulled one back on 87 through Jim McAlister to set up a tense finale.
The hosts counter-attacked down the right, and when Paul McGinn pulled the ball back, McCalister – racing into the box – buried it low past Gordon, who got a hand to the ball but could not keep it out.
But there was to be no equaliser and Celtic took a big step towards winning another title.