Arsenal will face Manchester City for the trophy at Wembley Stadium after ousting its London rival.
Granit Xhaka's second-half goal was enough to edge Arsenal past Chelsea and through to the Carabao Cup final.
The fixture was very much a game of two halves, with Chelsea taking ultimate control in the first 45 minutes, while Arsenal's persistence was the overriding force of the second.
Chelsea's started brightly, as Pedro played Hazard through to exploit poor organization from the home defense after only six minutes, putting the visitors in the driving seat with an away goal.
Arsenal stole one back moments, when Antonio Rudiger unfortunately deflected the ball into his own net, after a Nacho Monreal header had rebounded off Marcos Alonso, onto Rudiger and subsequently past a bemused Willy Caballero.
Arsenal's uncertainty at the back continued throughout the rest of the first half, as Chelsea dominated the next ten-minute period, without really threatening to re-take the lead.
Willian pulled up with a hamstring strain on the half-hour mark, an injury that paved the way for Chelsea's new signing Ross Barkley to make his debut for the club.
His debut during the game was also his first appearance in any competitive game this season; despite spending the first five months of the campaign as an Everton player.
The lack of attacking pressure from both sides was evident as half-time arrived, with only four shots on target in total.
The second half continued much like the first, as sporadic efforts from Arsenal punctuated Chelsea's general dominance of possession.
A rare forward advance from proved fruitful for Arsenal on the hour mark, as Lacazette's work-rate paid off, holding off Andreas Christensen to put the ball into the center as Granit Xhaka poked in to give the Gunners the lead.
Arsene Wenger's side then turned their game up to 11, and began to dominate proceedings. Alex Iwobi very nearly secured the win for Arsenal with a quarter of an hour remaining, but his effort on goal was well saved by Willy Caballero.
The Gunners were able to surprisingly shut up shop in the final ten minutes, and comfortably hold onto the their slender lead.
The victory sees Arsenal reach the League Cup final for the first time since 2011, when they lost 2-1 to Birmingham City.
Arsene Wenger's men now face Manchester City at Wembley Stadium on February 25th as they hope to make up for past mistakes and win the cup for the third time in the club's history.