It was goalless right up until the 80th minute when Bees skipper Pontus Jansson inadvertently bundled the ball into his own net following a cross from Reece James, and Jorginho sealed the deal from the spot just five minutes later.
The result sees Chelsea head into the semi-finals, with their next fixture in the competition likely in early January.
Story of the game
Brentford having two games postponed since their 2-1 victory over Watford just under two weeks ago gave them the opportunity to welcome back key players tonight, as Thomas Frank included Ethan Pinnock and Ivan Toney in the starting line-up and on the bench respectively after their bouts of Covid-19.
Meanwhile, Chelsea made eight changes to the side that drew at Wolverhampton Wanderers on Sunday, with head coach Thomas Tuchel opting to give opportunities to the club's next generation — Jude Soonsup-Bell (17), Xavier Simons and Harvey Vale (both 18) started for the European champions, with Charlie Webster and Lewis Hall also making the bench.
It was all Chelsea early on, the visitors having 83% of the possession 10 minutes in, but Brentford worked the first goalscoring chance when Bryan Mbeumo was unleashed behind the defence by Mathias Jensen. The Frenchman attempted to cut the ball across goal for strike partner Yoane Wissa, but it was a poor pass and the Blues were able to clear their lines.
The Bees had another opportunity just moments later when Rico Henry surged down the left flank and played the ball to Mbeumo on the edge of the box. Once again the 22-year old sought out Wissa and this time he found him with a chipped pass right onto the edge of the six-yard box — it looked a certain goal but for an outstanding save from Kepa Arrizabalaga.
They might have had lots of the ball, but it wasn't quite ticking for the youthful visitors. Soonsup-Bell provided the first bright attacking move with 17 on the clock when he weaved into the box and crossed for Ross Barkley in the centre, but the 28-year old skewed the resultant effort.
But it was Brentford who were certainly having the better of proceedings here. Henry was a constant thorn in the Blues defence with his belting runs down the left, and he caused them problems again when he darted to the byline before chipping a ball to Jensen on the penalty spot — however, once again, Arrizabalaga was equal to the effort.
It was going to take a moment of individual magic to break the deadlock in this match. Simons tried his luck with just over five minutes of the half remaining, taking aim from the edge of the box, but it was an easy save for Alvaro Fernandez.
Next, Brentford went straight down the other end with another surging run from Henry, picked out by a sumptuous pass from Jensen. He held off Simons as he made his way into the box and powered a strike at goal, but Arrizabalaga got out well to save.
There was when final chance before the break when an inch-perfect delivery from Azpilicueta found Vale unmarked in the box, but the teenager directed his header straight at a grateful Fernandez, and it would remain goalless heading into half-time.
Unhappy with his side's showing thus far, Tuchel shuffled his pack, with Jorginho and Christian Pulisic coming in for Mateo Kovacic and Soonsup-Bell — the latter had performed well enough considering his age and inexperience, so Chelsea's head coach was clearly pretty desperate for victory here.
The changes steadied Chelsea's ship somewhat, with Brentford camped in their own half after the break. The Blues came agonisingly close to break-in the deadlock when Saul Niguez crossed into the centre and the ball bundled inadvertently off Pulisic — it looked to be trickling in at the far post but for a brilliant save from Fernandez, who was also equal to Ross Barkley's follow-up.
Brentford introduced Toney and Norgaard just after the hour mark to indicate that they, too, were extremely keen to win this game before it headed straight to penalties at the end of the 90 minutes.
But, by and large, Chelsea remained on top, and they had another golden opportunity to open the scoring when Barkley picked up a loose ball in the box. His vicious half-volley deflected off Pinnock and missed the far post by a matter of inches.
Chelsea finally got their breakthrough on the 80th minute. Substitutes combined as Ngolo Kante fed James on the right flank and the Englishman delivered a tricky cross into the middle which was bundled awkwardly into his own net by Jansson.
And, like a London bus, after all that wait for a goal it looked like two would come along in a short space of time when Pulisic was felled in the area by Fernandez. Sure enough, Marriner pointed to the spot and Jorginho stepped up with a hop, skip and jump before sending the Spaniard the wrong way and securing his side's place in the semi-finals.
Tuchel's side weren't resting on their laurels. On the cusp of stoppage time Pulisic picked the ball up on the left edge of the box before cutting onto his favoured right foot and taking aim at the far top corner, but it whistled just wide of the target.
And that was how the game would finish as the travelling support serenaded their side into the semi-finals.
Takeaways from the match
Henry was Brentford's biggest attacking threat
Brentford's left wing-back Henry was more than a handful tonight, posing endless questions to Chelsea's defence and particularly the young Simons with the intelligence of his movement and ability to dart into action in a split-second.
Henry's pace alone made him a task to endure even for the superb Azpilicueta, and he created a number of changes attacking Chelsea's right side, particularly in the first-half, merely unlucky not to grab an assist tonight.
It's no surprise the winning goal came from the opposite side to him, either — Henry was shrewd defensively, marking Barkley virtually out of the game win the first-half and then given an even tougher challenge against Mason Mount for some of the second.
Vale shines brightest of Chelsea's youth contingent
This game perhaps came too early for Simons, something which perhaps demonstrates Chelsea's need for an adequate understudy to James — Tuchel surely didn't want to be forced into bringing him off the bench here after the amount he's played recently.
Soonsup-Bell looked more comfortable, holding the ball up well, but Vale lasted the longest of the three, and with good reason.
The 18-year old showed his technical ability tonight but what stood out most of all was his willingness to do the dirty work, snapping into tackles and tracking back to aid what was a resilient defensive display from the Blues.
Brentford: Fernandez; Pinnock, Jansson, Sorensen; Canos, Baptiste (Onyeka 74'), Jensen (Forss 82'), Janelt (Norgaard 65'), Henry (Ghoddos 74'); Mbeumo, Wissa (Toney 65').
Unused subs: Cox, Stevens, Thompson, Peart-Harris.
Chelsea: Arrizabalaga; Azpilicueta, Chalobah, Sarr; Simons (James 65'), Kovacic (Jorginho 46'), Saul, Alonso; Barkley (Kante 75'), Soonsup-Bell (Pulisic 46'), Vale (Mount 65').
Unused subs: Bettinelli, Rudiger, Hall, Webster.
Referee: Andre Marriner