Celtic overcame stubborn resistance in Kilmarnock to reach their sixth Viaplay Cup final in seven seasons.
Maeda’s light touch on Kyle Lafferty’s clearance attempt flew past Sam Walker to give holders Celtic the lead in the first half at Hampden.
The Japanese forward had another goal ruled out for offside, as did fellow countryman Reo Hatate.
Giorgos Giakoumakis settled the tie in stoppage time, moments after appearing to foul Joe Wright in the other box.
Kilmarnock will feel aggrieved that no penalty was awarded as they played their part in an absorbing semi-final.
Danny Armstrong was the club’s standout player from Ayrshire and had chances to level, including a close-range effort down the stretch that went just wide.
But Celtic saw victory and arranged a meeting with Rangers or Aberdeen – who play Sunday’s semi-final – on February 26 at the National Stadium.
Cup football is all about win or fail, drama and the unique nature of the occasion. Win, you progress, lose, you are eliminated.
Despite this simplicity and the opportunity available, the underdog often fails to muster the belief or the game plan to deliver a true contest. But amid a thrilling atmosphere and utterly horrific conditions in Hampden, Kilmarnock did just that.
A change of form and the intention to engage Celtic further up the pitch almost paid off after 30 seconds.
Armstrong surged down the right to expose the space vacated by Alexandro Bernabei. The winger reduced and sent a dangerous low ball through the penalty area. If Kyle Vassell had bet a second earlier, it was a certain goal. Unfortunately for Kilmarnock he didn’t and the opportunity was lost.
Armstrong started off as a possessed man as Derek McInnes’ team harassed and harassed but maintained a crucial threat.
Carl Starfelt’s laxity was captured by Rory McKenzie. He surged forward and unleashed a low push to the corner – only for Joe Hart to duck and flip around a post.
Celtic began to exert a grip on possession but failed to muddy Walker’s goal, until Lafferty’s attempted free-kick clearance hit Maeda who rushed and turned away into the corner superior.
It was a lucky break for Celtic, and they were expected to continue galloping.
But Kilmarnock immediately threatened with a header from Wright and then Liam Donnelly sent another header on a loop. If the goal was a knock, Kilmarnock’s headers weren’t made to bow.
Celtic regrouped at half-time and appeared to exert more pace to add to their possession. Hatate thought he added a second but was ruled offside after the ball deflected into his path.
Maeda then produced a wonderful finish into the top corner of Kyogo’s superb shot behind, but the assist had been delivered when the striker was slightly offside, and VAR intervened.
Josip Juranovic was then just wide of the target as Celtic searched for their elusive second goal.
But Kilmarnock never left. Armstrong came so close to the equalizer as he slid to the back post and then substitute Christian Doidge turned away on goal only for Hart to regain the ball.
Aaron Mooy and Liel Abada went close at the other end and, as time went on, you were never quite sure Celtic were over the line.
Even in injury time, a loud shout for a penalty caused panic as Giakoumakis joined in with Wright. Nothing was given, and then finally the second goal arrived.
When David Turnbull’s shot was saved, substitute teammate Giakoumakis couldn’t miss from close range.
Celtic got there – but were given an almighty challenge in a magnificent cup tie.
Player of the match – Daizen Maeda
Celtic do their job, Killie outstanding – analysis
If McInnes can instill that kind of performance in his team consistently, they’ll quickly move up from 11th in the standings. Much of what they produced was spot on except for the most crucial part, finding the back of the net.
They had chances, good ones, but just couldn’t convert. The desire to sometimes engage Celtic higher up the pitch and not give their opponents time to settle into their rhythm worked well. Their performance was outstanding.
Celtic will feel deserved to have had two goals, rightly ruled out for offside and plenty of chances to put the tie in earlier than them.
It was clear, however, that they were below their usual level. Whether this was due to conditions, Kilmarnock or something else is unclear.
However, they did what champions do. Has progressed to another cup final and is close to winning the trophy for the sixth time in seven seasons.
And after?
Celtic get back to league business by hosting St Mirren on Wednesday (19:45 GMT), while Kilmarnock take on Rangers at Rugby Park (20:00).
