Aberdeen scored first through Adam Rooney in the 27th minute but Stefan Johansen replied 10 minutes later and then Van Dijk secured the points in the dying minutes.
Celtic skipper Scott Brown had been sent off 10 minutes from time after picking up a second booking for over-zealous fouls.
The victory takes champions Celtic to the top of the table for the first time this season, above Inverness courtesy of their better goal difference, while Aberdeen stay in fifth place, four points off the joint leaders.
Aberdeen had an early penalty shout when Brown shoved aside Peter Pawlett on the edge of the box but referee Alan Muir ruled it was a fair challenge.
They then grabbed the opening goal through Rooney nearly half an hour into the game. Rooney was quickest to the ball after Lukasz Zaluska in the Celtic goal saved a shot but failed to hold it.
Rooney did not hit it all that cleanly but it scrambled in just inside the right-hand post.
Until that point it had been a fairly even and open game with a few firm tackles going in, as you would expect from a match between these two sides.
The Dons lost influential midfielder Willo Flood, who hobbled off with what appeared to be a hamstring injury, with Barry Robson on as his replacement.
Celtic, however, had been edging the possession and in the 38th minute, Johansen broke into the box on the left. Under pressure, as he was tackled, he just managed to chip the ball goalwards and past Dons keeper Scott Brown.
For Brown, that was the end of a sequence of clean sheets. The 29-year-old former Wolves and Cheltenham keeper had not conceded a goal until that point in what was his fifth appearance for Aberdeen.
The second half was a much tighter affair with few chances.
Niall McGinn hit a curling right-footed shot over the Celtic bar before breaking down the left in the 63rd minute and hitting a fierce shot which cannoned back off the near-side post.
The came Van Dijk’s winner. He stole into the back of the box, unmarked, from a corner to poke in a cross from Johansen and grab the goal that put the champions back on top of the table.
There was controversy immediately after the game when Aberdeen defender Shay Logan was red carded after the final whistle for using foul and abusive language.
Previously, Celtic winger Aleksandar Tonev had been given a seven-match suspension after being found guilty of racially abusing Logan when Celtic hosted Aberdeen in September.