The game saw three red cards, two goals, one missed penalty as well as two disallowed goals, but with a 1-1 draw on the night, it was the current holders of the trophy who made the final on May 27.
Luis Suarez gave Barcelona the lead with two minutes of the first half to play, with the hosts going down to 10 men 12 minutes after the restart with a second yellow card for Sergi Roberto before Yannick Ferreira Carrasco followed suit not long after.
Kevin Gameiro missed the chance to get Atletico level on the evening after missing an 80th-minute penalty, but atoned for his mistake two minutes later as he slotted past Jasper Cillessen.
And the topsy-turvy semi-final was capped off as Suarez was given his marching orders on the stroke of the 90th minute, but Atletico could not make their extra man count as Barca hung on to make the Copa del Rey final.
It was a fast start from the visitors, who were chasing their first Nou Camp victory in 11 years, with Antoine Griezmann seeing an effort blocked inside three minutes before Suarez fired into the side of the net at the other end not long after.
Barcelona goalkeeper Cillessen was a busy man in the opening exchanges, with Atletico initially testing him in the eighth minute. Koke burst down the pitch after a cleared Barcelona corner, laying the ball off to Carrasco who went for goal but it was straight at the stopper.
Four minutes later, Cillessen was at it again as Koke floated a fine free-kick into the box that Griezmann flicked into the path of Carrasco. The Barcelona 'keeper initially pushed away his header before getting low to smother the rebound as Atleti continued to ask questions of their hosts.
Koke and Diego Godin also had shots saved in quick succession by the Netherlands international, before Atletico stopper Miguel Angel Moya had his first touch of the ball in the 28th minute as Lionel Messi worked his way into space but his eventual shot landed into the hands of the goalkeeper.
But Barcelona broke the deadlock just before half-time as Messi burst towards the box, racing past three Atletico defenders, before going for goal from the top of the box. Moya did well to push it away, but Suarez was waiting to slot the rebound into the back of the net and extend the hosts' aggregate lead.
It was a fast and furious start to the second half from both sides but Barcelona went down to 10 men 12 minutes after the restart. Roberto received his second yellow card of the game after fouls on Torres and Filipe Luis with Griezmann nearly making the advantage count but his goal three minutes later was wrongly disallowed for offside.
It did not take long for the game to level out though as Atletico were also subject to a sending off in the 69th minute, as Carrasco also saw a second yellow card for a foul on Jordi Alba after a first-half offence on Turan.
Messi had a fairly quiet game by his standards, but could have scored one of the goals of the tournament with 12 minutes of normal time to play as he curled a fantastic free-kick towards goal, but it smashed against the crossbar. The visitors won a penalty minutes afterwards as Gameiro was fouled by Gerard Pique in the box.
The forward decided to go for it himself, but skied his spot kick over the crossbar much to his own anger and frustration. However, all was not lost for the Frenchman as he got Atletico level in the 82nd minute after a fine break into the box from Griezmann, who slid the ball into the path of his countryman to slot into the back of the net.
It was a busy end to the game for Suarez, as he had goal correctly ruled out for offside in the 86th minute before receiving his first yellow card 60 seconds later. As the game ticked to the 90-minute mark, the Uruguayan was given his marching orders after a coming together with Koke, which means the striker will now miss out for Barcelona in the final.
Luis Enrique's men will face either Alaves or Celta Vigo on May 27 as the two sides meet on Wednesday where they are level on a 0-0 aggregate score.