Several flares, fireworks and pyrotechnics prior to the eagerly-anticipated contest resulted in a 14-minute delay to allow the smoke to clear for both the players and the VAR technology.
Following a cagey start, Celtic broke the deadlock just before the half-hour mark when Cameron Carter-Vickers rose highest to head home the opener, before Maeda sat down Dons goalkeeper Dimitar Mitov and set up Japanese compatriot Kyogo Furuhashi to smash in a second.
Maeda then got his name on the scoresheet for the first time five minutes before the break, running behind Nicky Devlin and meeting a smart through-ball from Nicolas Kuhn before firing into the top corner from 10 yards out.
Thelin will have been seeking a major response from his Aberdeen players in the second half, but Brendan Rodgers's side had no intention of resting on their laurels, and any hopes of a Dons revival were extinguished nines minutes after the interval when Maeda tapped home a back-post rebound.
Kuhn curled a delightful left-footed strike into the top corner to put Celtic five in front just before the hour mark, and Maeda capped a memorable evening for both himself and the Hoops by completing his hat-trick five minutes from time with a close-range finish following a superb free-flowing move.
Clinical Celtic cruise past Aberdeen to reach League Cup final
Victory for Celtic, who have not lost any of their 13 domestic games this season, has seen the 21-time Scottish League Cup winners reach the final for the eighth time in the last 11 seasons, while last season's losing finalists Aberdeen have seen their impressive 16-game unbeaten run in all competitions under Thelin come to an end.
Speaking to Premier Sports after the match, Rodgers said: "It was a testament to our players. And the demands they have. They play every week in big games. We have to manage this group through every game.
"It was up to us to decide the game and the players did that. They were brilliant today. We were more aggressive in the second half. Aberdeen have had an excellent season, they will continue to work well I'm sure."
Commenting on his comical slip which resulted in a yellow card, Rodgers added: "To be fair, I was raging because we had given the ball away.
"I have my moments, like every manager. It was just the game, even though we were comfortable at 3-0.
"It was a deserved yellow card. The speed of the ball [was the issue]. I just wanted to keep the tempo of the game."
Celtic will face either holders Rangers or Motherwell, who meet at Hampden on Sunday, in the Scottish League Cup final on December 15.