Socceroos star Rogic strolled into the right hand side of the box before bringing the ball back onto his left foot and firing into the far bottom corner of the goal to open Celtic's account on 16 minutes.
Shortly after man of the match James Forrest doubled the Hoops' advantage before the halftime break.
Moussa Dembele added a third from the penalty spot after Anthony O'Connor brought down Forrest as Celtic wrapped up their landmark major trophy to the delight of the two influential midfielders.
Rogic was full of excitement to score a goal as Celtic secured a milestone trophy.
"I think the fans deserve it, we deserve it as the playing squad because we have worked hard all season - it's no less than we deserve," Rogic said.
"We won 3-0 but it's not easy against Aberdeen. They have pushed us very close in the last few years but I feel this season we have gone up a level, but there are days like this that you enjoy playing football."
Forrest was in agreement with the Australian and lauded his teammates.
"We are absolutely delighted, we have done brilliantly to get to the final and obviously winning it is tremendous and we are going to enjoy it.
"I thought we were really strong in the first half - we started really well and that set us off for the game and I am delighted we managed to win it.
"We are absolutely delighted to win another trophy for this club and buzzing to have won it."
The players may be delighted but manager Brendan Rodgers is hungry for more and is adamant the club, founded in 1888, should now target their next 100 trophies.
"That is what the great history of this club is based upon," Rodgers said.
"It makes the milestone, that century of trophies over the course of history.
"And now we have to look to the next one and start the next century of trophies and that will be important for the club
"But for now it is a great night for the Celtic supporters to celebrate, they must have enjoyed the performance and, as I say, we push for the next one."
Aberdeen boss Derek McInnes bemoaned the loss but said Celtic deserved their victory.
"We were beaten by the better team," he said.
"To take Celtic on in a final we can't afford to have some below-par performances, we have to be at the maximum. I don't think we quite got to that today."
