The Hoops lost 1-0 away to Ajax on Wednesday night to slump to the bottom of their Champions League section and leave qualification hopes up in the air.
However, van Dijk led the charge against the Staggies, heading in an Emilio Izaguirre cross past County goalkeeper Mark Brown in the 41st minute after threatening on three earlier occasions.
It was the 22-year-old's first goal in green and white since signing from Dutch side Groningen in the summer for around £2million - and in the 52nd minute he got his second when he headed in a Charlie Mulgrew corner.
County substitute Ivan Sproule reduced the deficit in the 67th minute, after replacing Mark Klok, but midfielder Joe Ledley helped himself to a brace of headers to underline what was an impressive response from the Parkhead side to their midweek disappointment.
As promised, Neil Lennon rung the changes for the trip to the Highlands
Skipper Scott Brown and midfielder Nir Biton returned from suspension as the former Celtic captain made five changes to the side which started in Holland.
Also into the team from Wednesday night came right-back Darnell Fisher, Ledley and striker Teemu Pukki as Anthony Stokes and Kris Commons started on the bench with Mikael Lustig, Georgios Samaras and Beram Kayal out altogether.
Van Dijk was involved in the visitors' first three real goal threats as the champions started with pace and purpose.
His header from a Mulgrew cross in the second minute was cleared away in a packed penalty area by Stuart Kettlewell and five minutes later a powerful drive from 25 yards tested Brown.
In the 19th minute, after the league leaders' early pressure had subsided, van Dijk got on the end of a Mulgrew free-kick from the left but headed wide under pressure from the County defence.
Biton took a turn in reaching a Mulgrew free-kick in the 29th minute but he fared no better, heading wide of the target before James Forrest knocked a cross from Izaguirre over the bar from 12 yards.
County looked happy enough to have weather the storm but offered little in attack.
Their first effort on goal came eight minutes from the break when defender Mihael Kovacevic headed a Graham Carey corner over the bar from 10 yards.
That shaft of optimism, however, preceded Celtic's opener which came in the 41st minute when Mulgrew's short corner arrived at Izaguirre and this time the Hoops' left-back shifted the ball to his right foot and flighted it over for van Dijk to head in off the post from eight yards.
There was still time before the interval for Brown to make a decent save from Biton's long-distance drive and even at that point there was a sense that the home side would take nothing from this game.
Van Dijk's second came all too easily after captain Brown won a corner with a deflected strike which struck the post and flew behind.
When Mulgrew flighted the ball over the Dutchman rose highest at the near post to head it into the net.
County nearly got a lifeline when Sproule, on the pitch for just two minutes, followed up to slam the ball into the net after Hoops keeper Fraser Forster had parried a Rocco Quinn drive.
However, three minutes later Ledley got his head on to an Izaguirre cross to make it 3-1 before again scoring with a header in the 73rd minute, this time from a Fisher cross.
Brown made a good fingertip save from Biton's header as the rampant visitors threatened to really turn the screw, before Ledley was only denied a hat-trick by a post.
- Sports & Recreation
- Charlie Mulgrew
- Emilio Izaguirre
- Joe Ledley
- Ivan Sproule