The Hoops knew a win against the Dons would see them top the table for the first time this season but found their hopes dented in the 27th minute when Adam Rooney fired the home side in front.
Stefan Johansen took advantage of some dithering defending to sneak home a 38th minute equaliser.
Aberdeen had the best of the second half chances with Niall McGinn coming close with a shot that smashed the base of the post before Celtic skipper Scott Brown was sent off in the 82nd minute for a second bookable offence.
However, the ten men of Celtic conquered up a winner in the 90th minute as van Dijk showed great skill to convert a Johansen corner past Aberdeen keeper Scott Brown.
The result moves Celtic top on goal difference of Inverness Caledonian Thistle, who defeated Hamilton 4-2 on Saturday, albeit the Hoops have a game in hand.
Celtic's midweek European exertions meant manager Ronny Deila made a host of changes
Strike partners Anthony Stokes and John Guidetti returned, fit-again James Forrest came in for his first start since August while Lukasz Zaluska took the place of the injured Craig Gordon in goal.
Aberdeen had an early penalty claim when Peter Pawlett went down in the box after tangling with Hoops skipper Scott Brown but referee Alan Muir ignored their pleas.
A free-flowing move involving Forrest, Guidetti, Johansen and Stokes had the Aberdeen defence chasing shadows and ended with the Irish striker sending a first-time shot inches wide of the post.
Substitute Barry Robson and McGinn both had efforts blocked before the Dons took the lead in the 27th minute through Rooney.
Considine's long throw-in caused consternations in the box and the ball eventually broke back to the defender inside the box
His initial shot was saved by Zaluska but the Celtic 'keeper spilled the ball into Rooney's path and his effort took a slight deflection off van Dijk on its way into the bottom corner of the net.
Celtic grabbed an equaliser in the 38th minute through Johansen
The Norwegian's first touch on a lovely pass from Stokes looked heavy but Ryan Reynolds dithering in defence allowed the Norwegian to sneak in and lift the ball over Dons 'keeper Scott Brown from a difficult angle.
The Hoops were buoyed by the goal and Johansen came close to adding another a couple of minutes later but his viciously drilled shot was well-saved by Brown.
Forrest then flashed a fierce left foot strike just over the bar as Celtic finished the first half strongly.
Aberdeen responded well in the second half and McGinn flashed a shot just over the bar and came even closer to firing the Dons in front when he smashed a low shot off the base of the post.
McGinn should have done better when he headed woefully wide under no pressure in the box before Zaluska kept out a Ryan Jack header after he got on the end of McGinn's chipped ball to the back post.
Brown saw red in the 82nd minute as he picked up a second booking for a foul on McGinn but it was the ten men of Celtic who grabbed a last minute winner as van Dijk showed good skill to side foot Johansen's corner past Brown from close range.
Source : AFP
Source: AFP