Captain Lewis Baker strikes deep into extra-time to send the west London club into Monday's final of the youth tournament against Aston Villa or Sporting Lisbon
The Blues had held a 3-1 lead with just five minutes remaining on the clock but Chuba Akpom and Serge Gnabry struck twice in four minutes to force an additional 30 before Blues skipper Lewis Baker scored with a couple of minutes remaining to seal his side's place in Monday's final.
Gnabry wasted a gilt-edged chance to open the scoring in the seventh minute as Blues goalkeeper Mitchell Beeney scuffed the ball straight to the German but recovered to smother the Arsenal starlet's effort.
However, soon after the Germany youth international was given too much room in midfield to thread a fine ball to right-back Hector Bellerin, who had burst up his wing. The former Barcelona trainee got to the byeline before cutting the ball across to Akpom, who tucked home from four yards.
The Blues responded well and, after the tricky Jeremie Boga was fouled by Martin Angha, captain Baker curled a brilliant 25-yard free kick just wide that had Gunners keeper Deyan Iliev scrambling to his left.
Chelsea came out for the second half with their tails up and were given the perfect chance to equalise from the penalty spot after substitute Connor Hunte cut the ball back to Ruben Loftus-Cheek, who was bundled over by Gnabry.
Baker took on responsibility for the spot kick but saw Iliev dive to his right and keep the effort out - however, Islam Feruz burst onto the end of the ball and tucked it in for his seventh of the tournament, making him outright leading goalscorer.
The Blues were energised by the goal and, after surviving a scare as Kristoffer Olsson lifted a 12-yard effort over the bar, they scored twice in three minutes to take the game away from Arsenal
Chelsea's second came from Baker as the midfielder hit a speculative effort from 35 yards that Iliev inexplicably allowed to bobble under his arms and into the back of the net.
With the Arsenal backline shaking, Alex Kiwomya zipped past Angha just inside the box and drilled the ball across goal where Boga was waiting at the far post to bundle home under pressure from Bellerin.
Arsenal desperately pushed for late goals and Zak Ansah whipped a ball in from the right that Akpom turned home to set up a nervy finish for the Blues.
And they could not hold on as Gnabry burst inside from the right wing and lashed a left-footed shot that gave Beeney absolutely no chance and take the game to extra time.
Alex Kiwomya almost scored in the first minute of the additional half-hour but he dragged an effort across goal with Feruz awaiting a tap-in in the middle of the box.
With just three minutes remaining before a penalty shootout, Chelsea grabbed the winner as John Swift nipped past Olsson on the right and cut the ball across goal where Baker was unmarked to touch home the winner that will see the Blues take on Aston Villa or Sporting Lisbon in Monday's final.