Ronny Deila's side responded to their shock Scottish Cup semi-final defeat to Inverness Caledonian Thistle on Sunday by edging to victory at Dens Park to go eight points clear of Aberdeen at the top of the table.
Mackay-Steven was cup-tied for that heartbreaking loss at the weekend, but the former Dundee United winger marked his return to the starting line-up by firing home with a clinical finish after 32 minutes.
Van Dijk then got in on the act when he curled home a free-kick just after the hour mark to give the Glasgow giants breathing space.
Jim McAlister reduced Dundee's arrears when the ball was cut back into his path three minutes from time, but the hosts were unable to salvage a point as Celtic marched on.
‘It was without a doubt one of the most important matches that I played in my career. It wasn’t just Champions League football – it was a whole club at stake’: Ex-Chelsea star opens up on key game which changed the Blues' fortunes forever
'I was Arsenal captain and really enjoyed it, but when Man City come calling, you have to listen': England international reveals reason for swapping London with Manchester
