Dylan Tait (far right) sealed Falkirk's win
Falkirk stunned top-flight Hearts to reach the Premier Sports Cup quarter-finals.
Ethan Ross and Dylan Tait's second-half goals eliminated last season's semi-finalists and continued Hearts' winless start to the campaign.
Steven Naismith's visitors created a glut of chances in the opening period and not even the second-half introduction of Lawrence Shankland could force a goal against the Championship newcomers.
John McGlynn's side, who had Ryan Shanley sent off late on, will discover their last-eight opponents when the draw is made on Sunday.
Liam Boyce shot over and Kenneth Vargas threatened twice in quick succession as Hearts started brightly, Vargas hitting the bar and drawing a save from Nicky Hogarth.
Gary Oliver forced Craig Gordon into action, the veteran Hearts goalkeeper making his first appearance of the season and getting off his line to make the block.
Yutaro Oda then went through on Hogarth's goal and the keeper prevailed with a foot block, as he did up against a Blair Spittal volley later on.
Falkirk broke immediately from the Spittal chance and Ross MacIver was denied when one on one with Gordon.
The pattern of play continued into the second half with Hearts seeing plenty of the ball in attacking areas and the Bairns keen to hit on the break.
And it was from one such attack that Ross found the net as he met Keelan Adams' low ball with an emphatic finish.
The goal took the wind out of Hearts' sails and they were not as threatening in the final half-hour.
MacIver was denied by another superb Gordon save as Falkirk threatened a second.
And a clincher arrived when Gordon was closed down by Alfredo Agyeman as he passed out of defence, allowing Calvin Miller to steal possession before squaring for Tait to finish.
Blow for Europe-bound Hearts
An early exit from the League Cup will be a massive frustration and another blow to confidence as Hearts enter the Europa League arena for the first time this season with a play-off first leg away to Czech side Viktoria Plzen on Thursday.
However, Hearts' start to the game belied their winless start to the Premiership campaign, with Oda and Vargas in particular causing the Bairns problems. They just couldn't take their chances.
The visitors were perturbed by a cynical challenge by Sean Mackie on Vargas that resulted in a yellow card, seeming to suggest it should have been red. Another flashpoint involved Vargas pushing Brad Spencer after being fouled. Both were booked.
Falkirk, one of the SPFL's form teams, were never overawed by the occasion and knew they had a strong home record to build on. They lost only twice at home last season, both in cup ties, and rarely looked like being undone after the Ross opener.
The match did end on a bit of a sour note as substitute Shanley was dismissed for catching Stephen Kingsley with a high foot.
What they said
Falkirk manager John McGlynn: "Very proud, very proud of the players. I thought they were enormous, different class. Amazing performance. We rode our luck early doors. Hearts hit the bar and big Nicky's made two or three good saves with his feet.
"When we rode that storm and got over that period, we grew into the game and caused Hearts problems. Second half, Hearts were not really creating a lot. Two-nil. They just continuously achieve, continually turn out these performances that are not flukes. There's such consistency in their play."
Hearts head coach Steven Naismith: "Ultimately we're really disappointed, we're out the cup. The tale of the game is you've got to take your chances. We create four really good chances in the first half but you've got to take them. Cup football is defined by that.
"The second goal absolutely kills us in terms of any sort of momentum. There's no excuse. We ultimately need to just put 11 players on the park that are going to win us the game and if that's keeping the same team or keeping the majority even with our tight schedule then we'll need to do that. It probably clears that part up, that we maybe can't rotate as much as we would've liked."
