The holders had two goals chalked off by VAR for offside after the break which kept Derek McInnes’ side in touch.
However, second-half substitute Giakoumakis – tipped to be on his way out of Parkhead – grabbed a second in the fifth minute of six added minutes to finish off a Killie side who had put in a determined display in the swirling wind and rain before coming up short against the Scottish champions.
Ange Postecoglou’s side will face either Rangers or Aberdeen in the final, with that last-four game taking place at the national stadium on Sunday.
Celtic ran out comfortable 2-0 winner when Killie visited Parkhead in the cinch Premiership at the weekend and there were few outside Rugby Park who gave the Ayrshire side a chance.
Killie striker Kyle Lafferty returned from his 10-game ban for being caught using sectarian language on video but he would inadvertently contribute to the opening Hoops goal.
However, Danny Armstrong had the Celtic defence in trouble in the opening moments.
There was less than 30 seconds played when stretching forward Kyle Vassell just missed a cross from the Kilmarnock winger, who then forced a corner which was headed behind by Liam Donnelly.
Celtic, with right-back Josip Juranovic in for Alistair Johnston, were put under pressure again when defender Carl Starfelt gave possession away to Rory McKenzie, who forced a fine save from Hoops goalkeeper Joe Hart with a low drive.
The Parkhead side began to assert themselves and soon took the lead.
When midfielder Mooy swung a free-kick into the box from the right, Lafferty’s attempted clearance from inside the six-yard box came off the chest of Maeda and into the net.
The Rugby Park side responded immediately and Hart saved a Joe Wright header before Donnelly headed the resultant corner over the crossbar, chances that McInnes’s side could ill afford to squander.
Christian Doidge and Liam Polworth took over from Lafferty and Donnelly for the start of the second half.
Celtic midfielder Reo Hatate had the ball in the net in the 49th minute but the goal was ruled out by VAR for offside and he sent a drive wide of the target from the edge of the box six minutes later.
Maeda beat Killie goalkeeper Sam Walker from 14 yards on the hour mark but VAR ruled the goal out for an earlier offside on fellow countryman Kyogo Furuhashi who had slipped him through.
Celtic were in control but – at the other end, following a Killie break – Armstrong hit the sidenetting on the stretch.
Postecoglou made a triple substitution with Giakoumakis, Liel Abada and Matt O’Riley on for Jota, Furuhashi and Hatate, with Kilmarnock’s Scott Robinson taking over from Vassell, just before Hart made a great save from Doidge’s close-range strike.
In the 83rd minute, as play stretched from end to end, Walker dived low to tip Mooy’s curling effort clear and then Abada missed the target with a header.
But – at the death – Giakoumakis, who might have given away a penalty when he clumsily challenged Wright inside the box, tapped the ball into an empty net after Walker spilled a shot from fellow Hoops substitute David Turnbull.