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Celtic needed less than five minutes to open the scoring as new signing Jason Denayer made the most of the Scottish champions' early dominance to fire in from close range.
Stefan Johansen made it three just six minutes later, stealing the ball on the edge of the box before drilling it into the back of the net.
Celtic's formidable display continued after the break as Charlie Mulgrew guided in a Stokes free kick less than 10 minutes after the restart.
Cardiff City loanee Berget made amends for his first-half miss with just over an hour gone, headed the ball home from an Efe Ambrose cross.
The visitors got one back in the 71st minute when John Rankin had a shot deflected into the back of the Celtic goal.
However, Celtic continued to apply the pressure, and added a sixth in stoppage time as Berget completed his brace, securing an emphatic win for the champions in their first home match of the season.