Celtic came from behind twice against Championship club Falkirk to survive a scare and set up a Scottish League Cup semi-final against Aberdeen.

Two goals in under three second-half minutes from striker Adam Idah proved decisive after a previously sloppy performance from Brendan Rodgers' side.

Championship leaders Falkirk already had two top-flight scalps in this competition and played with confidence in the opening stages, taking the game to Celtic.

Goals from Ross MacIver and Finn Yeats - either side of Paulo Bernardo's volley - gave John McGlynn's side a deserved half-time lead.

Rodgers made changes in the second half and the quality of his substitutes showed, as Nicolas Kuhn set up Idah twice, before scoring two of his own.

Michael McKenna was sent off late on for Falkirk as they were left to rue what might have been.

In the other semi-final, holders Rangers will face Motherwell. Both ties are to take place on the weekend of 2-3 November.

Rodgers made eight changes to the side that swept aside Slovan Bratislava in the Champions League, but it resulted in a disjointed first-half display.

The back four in particular were very shaky. Pacey forward Alfredo Agyeman got in behind new-look centre-back pairing Stephen Welsh and Auston Trusty with alarming ease, while Barcelona loanee Alex Valle made his debut at left-back and was questionable for both Falkirk goals.

In forward areas, Luis Palma struggled to have any real influence, constantly cutting inside on to his right foot instead of hitting the byeline, and his final ball was lacking.

The Celtic manager's displeasure was demonstrated by a quadruple substitution on the hour mark, with big-money signing Arne Engels introduced alongside Greg Taylor, Kuhn and Yang Hyun-Jun.

It had the desired effect as Celtic began to pin Falkirk in their own half and pop the ball about with confidence.

A rasping shot from Yang stung Nicky Hogarth's palms in the Falkirk goal, and not long after, Idah tapped home Kuhn's cross to level the scores.

Straight from kick-off, Celtic pinched possession high up the pitch and Kuhn fed Idah again. The Republic of Ireland international bullied his way past two would-be tacklers and swept beyond Hogarth to give Celtic the lead for the first time.

Kuhn has shone this season and he took his two goals superbly, dinking calmly over Hogarth after a well-weighted Engels through ball, before lashing in Celtic's fifth from the edge of the box.

Rodgers will be delighted to reach Hampden having gone 2-1 behind, and will be pleased with the way things came together in the closing stages.

However, some underwhelming displays from fringe members of his squad will have raised question marks over their suitability for games against higher-profile opposition.

Having taken the League 1 title at a canter last season, and won their first five league games this season, Falkirk came to Celtic Park sensing a monumental upset was on the cards.

They played Celtic at their own game in the first half, pressing high, passing out from the back and zipping the ball about with a real verve.

MacIver led the line wonderfully before being forced off through injury, and his strike to open the scoring will live long in the memory for the significant away support that travelled to Glasgow.

Agyeman was a constant threat with his runs in behind, and it was his pinpoint cross to the back post that Yeats nodded home to restore Falkirk's lead.

Yes, they tired and were eventually overwhelmed by Celtic's quality off the bench, but this performance will give McGlynn real belief his side have what it takes to secure back-to-back promotions.

Celtic manager Brendan Rodgers told Premier Sports: "It's always a risk making changes. You could see that connection wasn't quite there for the first hour.

"If there's any blame on the first hour, it's on me. I make the changes. Falkirk were aggressive and pressed us really well. Full credit to them.

"Looking at the Aberdeen results, they've been excellent. When it comes round, it will be a good game."

Falkirk manager John McGlynn: "I'm so proud of our guys and they can take a lot of plaudits from the game.

"We've got to take the positives. The players need to take inspiration from being here and want to be here more often."